Jim and Jessie running around the play ground.

Question

jim and Jessie are running around a play ground Jessie runs at 10 miles per hour. Jim runs at 7 miles per hour. If Jim starts running 2 hour early. How many hours will Jessie run to meet Jim.

Answer 1

Hi Kenneth, this is an application of the formula: d(istance) = r(ate) * t(ime). The distance traveled by both Jim and Jessie will be the same.

Distance for Jim:

d_Jim = r * t

d_Jim = 7 * (t + 2), remember Jim runs for 2 hours more than Jessie.

Distance for Jessie:

d_Jessie = r * t

d_Jessie = 10 * t

The distance, d, for Jim and Jessie is the same. Therefore, d_Jim = d_Jessie, or 7 * (t + 2) = 10 * t.

Solve for t:

7 * (t + 2) = 10 * t

7t + 14 = 10 t

14 = 3t

t = 14/3

It will take Jessie 14/3, or 4 and 2/3 hours to catch Jim.

Check:

7 * (14/3 + 2) = 10 * 14/3

7 * 20/3 = 10 * 14/3

140/3 = 140/3

Questions?

Answer 2

Hi Kenneth,

Setting up the equations to solve is the toughest part of this problem. The variable we are trying to solve for is the number of hours it takes for them to run the same distance (that's when they will meet). Let's call that variable "x".

Now, we can write one equation for the number of miles Jessie runs:

10x (where 10 is miles/hour, x is hours. miles/hour * hour gives miles)

The equation for the number of miles Jim runs is:

7x + 2*7. The 7x term is similar to the description above (miles/hour * hours = miles). The 2*7 comes in from the fact that Jim got a 2 hour head start. 2 hour head start running at 7 miles per hour gives 2*7 = 14 mile head start.

We can set these two equations equal to eachother, since we want the distance in miles that they both run to be the same: 10x = 7x + 14. Simplifying, we get 3x = 14. Therefore, x (the number of hours until they meet) = 14/3