SOLUTION: The distance between two places is 400 km. Pete travels half of the way by bus and the other half by train and it takes him 6 1/2 hours for the whole journey. Tom travels 300 km by

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Question 1172580: The distance between two places is 400 km. Pete travels half of the way by bus and the other half by train and it takes him 6 1/2 hours for the whole journey. Tom travels 300 km by bus and 100 km by train and it takes him 7 1/4 hours for the whole journey. Find the speed of the bus and the speed of the train.
Found 2 solutions by ankor@dixie-net.com, Solver92311:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The distance between two places is 400 km.
Pete travels half of the way by bus and the other half by train and it takes him 6 1/2 hours for the whole journey.
Tom travels 300 km by bus and 100 km by train and it takes him 7 1/4 hours for the whole journey.
Find the speed of the bus and the speed of the train.
:
let b = speed of the bus
let t = speed of the train
:
Write time equation for each
"Pete travels half of the way by bus and the other half by train and it takes him 6 1/2 hours for the whole journey."
200%2Fb + 200%2Ft = 6.5
multiply by bt
200t + 200b = 6.5bt
"Tom travels 300 km by bus and 100 km by train and it takes him 7 1/4 hours for the whole journey."
300%2Fb + 100%2Ft = 7.25
300t + 100b = 7.25bt
:
Use elimination, multiply the above by 2, subtract the 1st equation
600t + 200b = 14.5bt
200t + 200b = 6.5bt
----------------------subtraction eliminates b,
400t = 8bt
divide both sides by t
400 = 8b
b = 400/8
b = 50 mph is the speed of the bus
;
Find the time of the bus in the first trip
200/50 = 4 hrs
then
4 + 200%2Ft = 6.5
subtract 4 from both sides
200%2Ft = 2.5
find the speed of the train
2.5t = 200
t = 200/2.5
t = 80 mph is the speed of the train
:
:
Check the solutions in the 2nd trip
300%2F50 + 100%2F80 =
6 + 1.25 = 7.25 hr

Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Let the speed of the bus and the speed of the train.

Distance equals rate times time, which is to say time is equal to distance divided by rate. Hence, is the time it takes the bus to go 200 km, and is the time it take the train to go 200 km. We know these two times add up to 6.5 hours, hence:



Similarly,



Multiply the second equation by -2, and add the two equations to get:



Solve for . The rest is just arithmetic.

John

My calculator said it, I believe it, that settles it

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