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A bus left San Diego a 1:30 and traveled 50 mph a train left San Diego at 3:30 traveling in the same direction at 70 mph at what time does the train catch up with the bus

User Ttkalec
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1 Answer

5 votes

Equations

The distance x traveled by an object moving at a speed v during a time t is given by:

x = v.t

The bus left San Diego at 1:30 at a speed of 50 mph. A train left San Diego at 3:30 in the same direction at 70 mph.

Note the train left 2 hours later than the bus. This allowed the bus to travel a distance of:

x = 50 * 2 = 100 mi

So the bus is 100 miles ahead of the train at 3:30 pm.

Now let's assume that t more hours pass.

The bus will travel a distance of

xb = 50.t

The train travels a distance of:

xt = 70.t

For the train to catch up with the bus, its distance must be equal to the distance of the bus plus the 100 miles it's ahead of the train, thus:

70.t = 50.t + 100

When we solve this equation for t, we will know the number of hours needed. Subtracting 50.t:

70.t - 50.t = 100

Operating:

20.t = 100

Dividing by 20:

t = 100/20

t = 5

This means that 5 hours must pass for the train to catch up with the bus. Since the train left at 3:30, that will happen at 8:30

User Jonas Geiregat
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