SOLUTION: On a trip, Debbie spent as much time on the train as she did on the bus. the train averaged 50 miles per hour and the bus averaged 35 miles per hour. If she went 105 miles more on

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Question 75974: On a trip, Debbie spent as much time on the train as she did on the bus. the train averaged 50 miles per hour and the bus averaged 35 miles per hour. If she went 105 miles more on the train, how far did she go altogether?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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On a trip, Debbie spent as much time on the train as she did on the bus. the train averaged 50 miles per hour and the bus averaged 35 miles per hour. If she went 105 miles more on the train, how far did she go altogether?
:
Let x = distance by bus; then (x+105) = distance by train
:
Write a time equation; time = distance/speed
:
Train time = Bus time
%28%28x%2B105%29%29%2F55 = x%2F35
:
Cross multiply and you have:
55x = 35(x+105)
:
55x = 35x + 3675
55x - 35x = 3675
20x = 3675
x = 3675/20
x = 183.75 miles by bus
:
183.75 + 105 = 288.75 mi by train
:
183.75 + 288.75 = 472.5 mi total distance
:
:
Check solution by finding the times, they should be equal:
Bus time: 183.75/35 = 5.25 hrs
Train time:288.75/55 = 5.25 hrs