If a parade 1 mi long is proceeding at 4 mph, how long will it take a runner, jogging at 6 mph, to travel from the end of the parade to the start of the parade?

Question

My answer must be in the units of miles. 

Answer 1

Let x = miles traveled by the person at the start of the parade line when the runner reaches the start of the line.

Then the runner will have traveled x + 1 miles

 

The time for both is the same.

 

Distance = speed x time

 

or

 

time = distance /speed

 

We set the times equal to each other.

 

x/4mph = (x + 1)6mph    now cross multiply

 

4(x + 1) = 6x

4x + 4 = 6x

2x = 4

x = 2 miles

x + 1 = 3 miles

 

Therefore travel time = 3miles / 6mph = .5 hours

 

 

 

Answer 2

Remember rate * time = distance. the parade has traveled 4t miles but has a 1 mile head start. The jogger traveled 6t. So,

4t +1 = 6t or t = 1/2 hour. Your question asked how long which is a unit of time so 1/2 is your answer. Let's check though. In 1/2 an hour the front of the parade will have traveled 2 miles but if someone had to catch up, he would have to travel the length of the parade plus these 2 miles resulting in 3 miles. the jogger traveled 3 miles in that same 1/2 hour so he did catch up.