Question

Mr. Howard and Ms. Egan enjoy running on the weekends. They both usually run at a steady pace and try to meet in the middle. They are 14 miles apart. Mr. Howard can run 3 miles in 30 minutes. Ms. Egan can run 4 miles in 30 minutes.

Answer 1

Given :

Distance between them, D = 14 miles .

Mr. Howard can run 3 miles in 30 minutes.

Ms. Egan can run 4 miles in 30 minutes.

To Find :

Time taken by them to meet.

Solution :

Mr Howard speed, $v_H=\dfrac{3}{0.5}=6\ mph$ .

Mr Egan speed, $v_e=\dfrac{4}{0.5}=- 8\ mph$ . [ Since they run in opposite direction ]

Their relative speed :

$v=v_E-v_H\\\\v = 8-(-6) \ mph \\\\v = 14 \ mph$

Time taken by them to meet :

$T = \dfrac{14}{14}\ hours\\\\T = 1 \ hours$

Hence, this is the required solution.