SOLUTION: Wendy took a trip to Davenport to Omaha, a distance of 300 mi. She traveled part of the way by bus, which arrived at the train station just in time to complete her journey by train

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Question 90404: Wendy took a trip to Davenport to Omaha, a distance of 300 mi. She traveled part of the way by bus, which arrived at the train station just in time to complete her journey by train. The bus average 40 mi/hand the train 60 mi/h. the entire trip took 51/2 h. How long did Wendy spend on the train?
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Wendy took a trip to Davenport to Omaha, a distance of 300 mi. She traveled part of the way by bus, which arrived at the train station just in time to complete her journey by train. The bus average 40 mi/hand the train 60 mi/h. the entire trip took 51/2 h. How long did Wendy spend on the train?
Let distance covered by bus be = x mi
Then distance covered by train = 300-x mi
speed of the bus = 40 mi/h
time taken by bus to cover a distance of x mi = dist/speed = x/40 hr

speed of the train = 60 mi/h
time taken by the train to cover a distanc of (300-x) = (300-x)/60 hr
Total time taken to covera distance of 300 miles = 51/2 nr = 11/2 hr
x/40+(300-x)/60 = 11/2
l.c.m of 40,60 = 120 3x+2(300-x)/120 = 11/2
3x+600-2x/120 = 11/2
( x+600)2 = 11*120
divide by 2 on both sides we get x+600 = 11*60 = 660
x = 660-600 = 60 miles

distance covered by bus = 60 miles
distance covered by train = 300-60 = 240 miles
Time spent in train = 240/60 = 4 hrs