Andy C. answered • 09/29/17

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Math/Physics Tutor

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.