Simple algebraic question: homework
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Two boats, Boat A and Boat B, leave a boat dock, with Boat B departing 15 minutes after Boat A. Boat A maintained a constant speed of 15 miles per hour while traveling the 10-mile distance across the lake, while Boat B maintained a constant speed of 25 miles per hour over the same route. At what mile location of the route did Boat B pass Boat A?
algebra-precalculus
asked Nov 19 at 1:33
Daniel
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Two boats, Boat A and Boat B, leave a boat dock, with Boat B departing 15 minutes after Boat A. Boat A maintained a constant speed of 15 miles per hour while traveling the 10-mile distance across the lake, while Boat B maintained a constant speed of 25 miles per hour over the same route. At what mile location of the route did Boat B pass Boat A?
algebra-precalculus
asked Nov 19 at 1:33
Daniel
6
1
You should post some of your own insights or attempts before asking a homework question.
– dyf
Nov 19 at 1:39
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Two boats, Boat A and Boat B, leave a boat dock, with Boat B departing 15 minutes after Boat A. Boat A maintained a constant speed of 15 miles per hour while traveling the 10-mile distance across the lake, while Boat B maintained a constant speed of 25 miles per hour over the same route. At what mile location of the route did Boat B pass Boat A?
algebra-precalculus
asked Nov 19 at 1:33
Daniel
6
Two boats, Boat A and Boat B, leave a boat dock, with Boat B departing 15 minutes after Boat A. Boat A maintained a constant speed of 15 miles per hour while traveling the 10-mile distance across the lake, while Boat B maintained a constant speed of 25 miles per hour over the same route. At what mile location of the route did Boat B pass Boat A?
algebra-precalculus
algebra-precalculus
asked Nov 19 at 1:33
Daniel
6
asked Nov 19 at 1:33
Daniel
6
asked Nov 19 at 1:33
Daniel
6
asked Nov 19 at 1:33
Daniel
6
asked Nov 19 at 1:33
Daniel
6
6
1
You should post some of your own insights or attempts before asking a homework question.
– dyf
Nov 19 at 1:39
add a comment |
1
You should post some of your own insights or attempts before asking a homework question.
– dyf
Nov 19 at 1:39
1
1
You should post some of your own insights or attempts before asking a homework question.
– dyf
Nov 19 at 1:39
You should post some of your own insights or attempts before asking a homework question.
– dyf
Nov 19 at 1:39
add a comment |
1 Answer
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If we let $t$ denote the time in hours after departure, Boat A left at time $t = 0.25$. The boats have speeds of 15 miles per hour (Boat A) and 25 miles per hour (Boat B). Equationally, we can represent these as
- $f_A(t) = 15t + (0.25 cdot 15)$
- $f_B(t) = 25t$
where $f_A(t),f_B(t)$ represent the distance traveled in miles. The coefficients of $t$ are the rates of travel, and the constant for $f_A(t)$ denotes the "head start" Boat A got (a quarter hour, at 15 mph).
Your goal is to find when Boat A and B had their paths cross. Equationally, this would be when $f_A(t) = f_B(t)$, assuming that $f_A(t),f_B(t)$ are between $[0,10]$. You're then asked to figure out at which location this crossover happened; this would correspond to plugging the $t$ into an equation to get the distance.
answered Nov 19 at 1:38
Eevee Trainer
1,549216
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
If we let $t$ denote the time in hours after departure, Boat A left at time $t = 0.25$. The boats have speeds of 15 miles per hour (Boat A) and 25 miles per hour (Boat B). Equationally, we can represent these as
- $f_A(t) = 15t + (0.25 cdot 15)$
- $f_B(t) = 25t$
where $f_A(t),f_B(t)$ represent the distance traveled in miles. The coefficients of $t$ are the rates of travel, and the constant for $f_A(t)$ denotes the "head start" Boat A got (a quarter hour, at 15 mph).
Your goal is to find when Boat A and B had their paths cross. Equationally, this would be when $f_A(t) = f_B(t)$, assuming that $f_A(t),f_B(t)$ are between $[0,10]$. You're then asked to figure out at which location this crossover happened; this would correspond to plugging the $t$ into an equation to get the distance.
answered Nov 19 at 1:38
Eevee Trainer
1,549216
add a comment |
up vote
1
down vote
If we let $t$ denote the time in hours after departure, Boat A left at time $t = 0.25$. The boats have speeds of 15 miles per hour (Boat A) and 25 miles per hour (Boat B). Equationally, we can represent these as
- $f_A(t) = 15t + (0.25 cdot 15)$
- $f_B(t) = 25t$
where $f_A(t),f_B(t)$ represent the distance traveled in miles. The coefficients of $t$ are the rates of travel, and the constant for $f_A(t)$ denotes the "head start" Boat A got (a quarter hour, at 15 mph).
Your goal is to find when Boat A and B had their paths cross. Equationally, this would be when $f_A(t) = f_B(t)$, assuming that $f_A(t),f_B(t)$ are between $[0,10]$. You're then asked to figure out at which location this crossover happened; this would correspond to plugging the $t$ into an equation to get the distance.
answered Nov 19 at 1:38
Eevee Trainer
1,549216
add a comment |
up vote
1
down vote
up vote
1
down vote
If we let $t$ denote the time in hours after departure, Boat A left at time $t = 0.25$. The boats have speeds of 15 miles per hour (Boat A) and 25 miles per hour (Boat B). Equationally, we can represent these as
- $f_A(t) = 15t + (0.25 cdot 15)$
- $f_B(t) = 25t$
where $f_A(t),f_B(t)$ represent the distance traveled in miles. The coefficients of $t$ are the rates of travel, and the constant for $f_A(t)$ denotes the "head start" Boat A got (a quarter hour, at 15 mph).
Your goal is to find when Boat A and B had their paths cross. Equationally, this would be when $f_A(t) = f_B(t)$, assuming that $f_A(t),f_B(t)$ are between $[0,10]$. You're then asked to figure out at which location this crossover happened; this would correspond to plugging the $t$ into an equation to get the distance.
answered Nov 19 at 1:38
Eevee Trainer
1,549216
If we let $t$ denote the time in hours after departure, Boat A left at time $t = 0.25$. The boats have speeds of 15 miles per hour (Boat A) and 25 miles per hour (Boat B). Equationally, we can represent these as
- $f_A(t) = 15t + (0.25 cdot 15)$
- $f_B(t) = 25t$
where $f_A(t),f_B(t)$ represent the distance traveled in miles. The coefficients of $t$ are the rates of travel, and the constant for $f_A(t)$ denotes the "head start" Boat A got (a quarter hour, at 15 mph).
Your goal is to find when Boat A and B had their paths cross. Equationally, this would be when $f_A(t) = f_B(t)$, assuming that $f_A(t),f_B(t)$ are between $[0,10]$. You're then asked to figure out at which location this crossover happened; this would correspond to plugging the $t$ into an equation to get the distance.
answered Nov 19 at 1:38
Eevee Trainer
1,549216
answered Nov 19 at 1:38
Eevee Trainer
1,549216
answered Nov 19 at 1:38
Eevee Trainer
1,549216
answered Nov 19 at 1:38
Eevee Trainer
1,549216
1,549216
add a comment |
add a comment |
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You should post some of your own insights or attempts before asking a homework question.
– dyf
Nov 19 at 1:39