Question

Two bicyclists were racing toward each other when they were 98 miles apart. Three hours later they did not meet yet and the distance between them was 2 miles. How fast did they bike if one was 3mph slower than the other.

Answer 1

Let, speed of 1st bicyclist is x.

So, speed of 2nd bicyclist is x-3 .

We know, relative speed when two objects moves towards each other :

$v = x + ( x-3 )\\\\v = 2x - 3$

Now, distance travelled in 3 hours is (98-2) miles .

So,

$2x-3 = \dfrac{96}{3}\\\\2x - 3 = 32\\\\2x = 35\\\\x = 17.5\ mph$

Therefore, speed of bikes are 17.5 mph and 14.5 mph.

Hence, this is the required solution.