Question

Michelle is now 50 miles ahead of John.

Michelle is traveling at a constant rate. John is traveling in the same direction, at a rate 10 miles per hour faster than Michelle. In how many hours will John catch up to Michelle?
A. 6
B. 5
C. 2
D. 0
E. John can't catch up to Michelle

Answer 1

Let's call Michelle's speed "M" and John's speed "J". We know that John's speed is 10 miles per hour faster than Michelle's speed, so we can express this as:

J = M + 10

We also know that Michelle is 50 miles ahead of John, so we can express this as:

Distance = 50 miles

Now we can use the formula:

Distance = Rate x Time

We want to know how long it will take John to catch up to Michelle, so we can call this time "t". We can use the formula for both Michelle and John, and set their distances equal to each other since they will meet at the same point:

M * t + 50 = J * t

Now we can substitute J with M + 10, and simplify:

M * t + 50 = (M + 10) * t

M * t + 50 = M * t + 10t

50 = 10t

t = 5

Therefore, John will catch up to Michelle in 5 hours (answer choice B).