Wendy took a trip from city A to city B, a distance of 220 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 30 mi/h, and the train averaged 85 mi/h. The entire trip took 5 1 2 h. How long did Wendy spend on the train?

1.72 hours on the train.

Step-by-step explanation:

The distance between the two cities is 220 miles. Therefore the sum of the bus and train distances is 220 miles. Let x be the distance by train and y the distance by bus: x + y = 220

Bus speed was 30 mph and train speed was 85 mph. The whole trip was 5 1/2 hours, that is 5.5 hours.

We have to, the bus distance would be equal to:

y = 260 - x

speed equals distance over time, like so:

v = d / t; if we rearrange for time

t = d / v, we can do another equality, since we know that the total time is 5.5 hours

5.5 = x / 85 + (260 - x) / 30; reorganizing we have left that:

(30 * x + 85 * 260 - 85x) / 85 * 30 = 5.5

Solving:

-55 * = 2550 * 5.5 - 22100

x = 146.81

146.81 miles would be the train distance.

To find the time, we divide by the speed of the train which is 85 mph:

146.81 / 85 = 1.72 h

We buy, with the equation the time:

146.81 / 85 + (260 - 146.81) / 30 = 5.5 hours

Therefore, Wendy takes 1.72 hours on the train.