Question

Lisa walks to the mall from her house at 5 mph. 10 minutes later, Lisa's sister Megan starts ridding her bike at 15 mph (they live at the same house) to the mall to meet up with Lisa. They arrive at the mall at the same time. How far is the mall from the house? How long did it take for Megan to get to the mall

Answer 1

1.25 meters

5 minutes

Explanation:

Firstly, we are asked to calculate how far the mall as to the house.

Let’s say the time taken by Lisa is x minutes to the mall. This means that the time taken by Megan would be (x-10) minutes since she is traveling at a much more greater speed.

Now, we convert their times to hours by dividing by 60.

Their distances traveled are equal. The total distance traveled by Lisa would be speed * time = 5 * x/60 = x/12

Megan’s distance = 15 * (x-10)/60 = (x-10)/4

Since the distances are same, we simply equate both;

x/12 = (x-10)/4

4x = 12x-120

8x = 120

x = 120/8

X = 15 minutes

Now, checking the distance from the mall to the house, we can use Lisa’s work rate and that is 5mph * 15/60 = 5 * 1/4 = 5/4 = 1.25meters

If we had use Megan’s rate = 15 * 5/60 = 15/12 = 1.25 meters

Time taken for Megan to get to the mall is x-10 minutes = 15-10 = 5 minutes