Riding bicycles

Question

Two cyclists, 42 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?

Answer 1

I'll walk you through this problem with different numbers. The same procedure will work for this example, but it will also allow you to see it without being able to get the answer without doing any Math.

For my example, I will have the cyclists 60 miles apart taking 4 hours to reach each other.

The first step in solving this problem is to write out the cyclists' speeds with the equation C + 2C = 60 where the distance cyclist 1 covers, C, is half of cyclist 2.

Using this equation, we find that 3C = 60 and C = 20

THat means cyclist 1 travelled 20 miles where cyclist 2 travelled 40 miles

We can double-check this by seeing that 20 + 40 = 60

Finding speed is a matter of dividing distance and time S = D/T

For each cyclist, the time, T, is 4 hours, but each cyclist travelled a different distance.

Cyclist 1 travelled 20 miles in 4 hours while cyclist 2 travelled 40 miles in the same 4 hours.

Our speed calculation tells us that Cyclist 1 went 5 mph (20 / 4 = 5) and cyclist 2 went 10 miles per hour (40 / 4 = 10)

I hope this helps, and if you have any other questions I would be happy to answer them.

Answer 2

d = rt, and together they travel 42 miles.

42 = (r + 2r)2

42 = 3r(2)

42 = 6r

r = 7

7(2) = 14 mph