How did Wendy spend on the train?

Question

Wendy took a trip from one city to another, a distance of 170 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 40 mi/h, and the train averaged 70 mi/h. The entire trip took 3 1 2 h. How long did Wendy spend on the train

Answer 1

distance = rate x time

 

Let time t be the time it takes by bus.

 

distance by bus = 40 mi/hr * t

 

distance by train = 70 mi/hr * (3.5 - t)

 

170 = distance by bus + distance by train

 

      = 40 mi/hr * t +  70 mi/hr * (3.5 - t)

 

      = 40 t + 245 - 70t     <---- distributive property; hours cancel when multiplying by time

 

      = 245 - 30t

 

-75 = -30 t

 

-75/-30 = t

 

5/2 = t

The time on the bus was 5/2 hr or 2 and 1/2 hours = 2.5 hours = 2 hours and 30 minutes.

 

The time on the train was 3 and 1/2 - 2 and 1/2 = 7/2 - 5/2 = 3.5 - 2.5 = 1 hour

 

 

 The bus went 40 mi/hr * 5/2 hours = 100 miles.

  The train went 70 miles/hr for 1 hour = 70 miles.

  The total distance of 170 miles in 3 and 1/2 hours.