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.
:
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/b}}} + {{{200/t}}} = 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/b}}} + {{{100/t}}} = 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/t}}} = 6.5
subtract 4 from both sides
{{{200/t}}} = 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
{{{300/50}}} + {{{100/80}}} =
6 + 1.25 = 7.25 hr