#### poppaqball

##### New member
I can't seem to figure this story problem out. Here it is:

In a run for charity Mary runs at a speed of 4mph. John leaves 12 minutes after Mary and runs 6mph. How long will it take for John to catch up with Mary?

#### masters

##### Full Member
poppaqball said:
I can't seem to figure this story problem out. Here it is:

In a run for charity Mary runs at a speed of 4mph. John leaves 12 minutes after Mary and runs 6mph. How long will it take for John to catch up with Mary?
Hi poppaqball,

Let's let t = the time Mary runs at the rate of 4 mph.

Then, John leaves 12 minutes later. Convert 12 minutes to hours and you get .2 hours.

This means John will travel (t - .2) at the rate of 6 mph.

When he catches up with Mary, they will have both run the same distance.

Using D = rt, Mary's distance is stated as D = 4t. John's distance is stated as D = 6(t - .2).

Setting the two distances equal to each other, we have:

$$\displaystyle 4t=6(t-.2)$$

Solve for t, which is in hours, and then convert to minutes.

#### poppaqball

##### New member
Thanks for the help. Although my teacher came up with 4t+.8=6t which ends up being 24 minutes. Is that correct? I got 36 minutes.

This is the second time shes done things backwards...unless I'm missing something.

Nevermind, Thanks for the help! I see what the problem was, I was solving for John not Mary.

Staff member