Word Problem, define variable, create equation, & solve

Question

Train A leaves a station at 8:00 and travels at 100km per hour towards the next city. One and a half hours later, Train B, an express leaves the same station traveling at 160 km per hour along the same route. At what time will train B overtake the slower train?

Answer 1

The distance formula is given by distance = rate(time) or d = rt

 

Train A leaves at 8:00 at a rate of 100 km/hr

If it travels for a time "t" hours the distance will be

d = 100t

 

Train B leaves 1.5 hours later at a rate of 160 km/hr

The time it will have travelled when the trains meet

will be 1.5 hours less than the time train A has travelled

or t-1.5  so the distance will be

d = 160(t-1.5)   when they meet

 

We need to find when these distances are the same so set them equal

 

100t = 160(t-1.5)

100t = 160t - 240

60t = 240

t = 4 hours

 

When train A has been travelling 4 hours 

and train B has been travelling 4-1.5 = 2.5 hours

the trains will meet.  4 hours from 8:00 is 12:00 and

2.5 hours from 9:30 is also 12:00

 

The answer is the faster train will overtake the slower train at 12:00

 

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Check the answer:  Both should have gone the same distance

 

Train A:  100(t) = 100(4) = 400 km  at 12:00

Train B:  160(t-1.5) = 160(4-1.5) = 160(2.5) = 400 km at 12:00

 

At 12:00 the trains will both have travelled 400Km from the station