Question 972443: Some travelers went 3 hours by car and 5 hours by train, passing 510 km during the whole ride. We know that they went 90 kilometers more by train than by car. Find the rate of the train and the rate of the car.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Some travelers went 3 hours by car and 5 hours by train, passing 510 km during the whole ride.
We know that they went 90 kilometers more by train than by car.
Find the rate of the train and the rate of the car.
:
let c = rate of the car
let t = rate of the train
:
Write a distance equation
" 3 hours by car and 5 hours by train, passing 510 km during the whole ride. "
3c + 5t = 510
:
"they went 90 kilometers more by train than by car."
5t - 3c = 90
:
Arrange the two equations for elimination
5t + 3c = 510
5t - 3c = 90
---------------Addition eliminates c, find t
10t + 0 = 600
t = 600/10
t = 60 km/hr is the rate of the train
:
Use the 1st equation to find c, replace t with 60
3c + 5(60) = 510
3c + 300 = 510
3c = 510 - 300
3c = 210
c = 210/3
c = 70 km/hr is the rate of the car
:
:
Check this in the 2nd equation; replace t and c
5(60) - 3(70) = 90
300 - 210 = 90
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