# Two men leave house at the same time but travel in opposite directions. Mr.Q's average rate is 3 miles per hour faster than Mr.H's. Find the rates at which they drive if after 5 hours they are...

Two men leave house at the same time but travel in opposite directions. Mr.Q's average rate is 3 miles per hour faster than Mr.H's. Find the rates at which they drive if after 5 hours they are 435 miles apart.

Let the driving speed of Mr. Q be Vq and that of Mr. H is Vh.

Using the given information, Mr. Q drives 3 mile/hr faster than Mr. H, which means

Vq = Vh + 3

After travelling in opposite directions for 5 hours, they are 435 miles apart. Now, since they are travelling in opposite directions, the sum of the distance traveled by each of them is equal to 435 miles, (the separation between the two, after 5 hours).

Distance traveled is given as the product of speed and time (5 hours)

Distance traveled by Mr. Q in 5 hrs = 5 x Vq = 5 x (Vh + 3)

Distance traveled by Mr. H in 5 hrs = 5 x Vh

and using the above logic, 5 x Vq + 5xVh = 435

or 5(Vq+Vh) = 435

or 5 (Vh+3+Vh) = 435

or 2Vh + 3 = 435/5 = 87

or 2Vh = 87-3 = 84

or **Vh = 84/2 = 42 miles/hr** and **Vq = Vh+3 = 45 miles/hr**

Mr. H's average rate can be expressed as: x mph

Mr. Q's average rate can be expressed as: x+3 mph

with 5 hours, Mr. H would have driven:

5 hours * x mph = 5x miles

with 5 hours, Mr. Q would have driven:

5 hours * x+3 mph = 5x+15 miles

Since they drove 435 miles in total together, it means that:

5x + 5x+15 = 435

Simplifying, you get:

10x = 420

= x = 42

Plug the value of x in both their rate to get:

Mr. H's average rate = 42 mph

Mr. Q's average rate = 45 mph