```Question 252651
Peter left the office with his motorbike at a rate of 40kph after one hour, Alex also left the office with his motor bike at a rate of 50kph. In how many hours will Alex overtake Peter?
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First let's do it in our head. Then we'll do it using algebra.

After 1 hour, Peter is 40 km away from Alex.
Alex then goes 10 kph faster. Therefore, he
approaches Peter at 10 kph, so it will take
him 4 hours to make up the 40 km head start.

Using algebra:

Let x = the time it will take Alex to overtake Peter

Make this chart:

DISTANCE      RATE     TIME
Peter
Alex

Peter travels x hours, and Alex travels x+1 hours.
So fill those in.

DISTANCE      RATE     TIME
Peter                             x
Alex                             x+1

Fill in their rates:

DISTANCE      RATE     TIME
Peter                   40       x+1
Alex                    50        x

Use DISTANCE = RATE * TIME to fill un the DISTANCES

DISTANCE      RATE     TIME
Peter    40(x+1)        40       x+1
Alex      50x           50        x

They went the same distance so set them equal:

40(x+1) = 50x
40x+40 = 50x
40x = 50x-40
-10x = -40
x = 4

So the answer is 4 hours, the same as when we did it