Question

Jane travels 4 times as fast as Gloria. Traveling in opposite directions, they are 175 miles apart after 2.5 hours. Find their rates of travel.

Answer 1

• Gloria's rates of travel: 14 mph

,

• Jane's rates of travel: 56 mph.

Explanation:

• Let Gloria's rate of travel = x

Jane travels 4 times as fast as Gloria, therefore:

• Jane's rate of travel = 4x

The time for which both have traveled = 2.5 hours

`\begin{gathered} \text{Distance=Rates}* Time \\ \text{Distance covered by Gloria}=2.5x \\ \text{Distance covered by Jane}=2.5(4x) \end{gathered}`

Since they are traveling in opposite directions, the total distance covered is the sum of the individual distance.

`175=2.5x+2.5(4x)`

Then, solve for x.

`\begin{gathered} 12.5x=175 \\ x=(175)/(12.5) \\ x=14 \end{gathered}`

Therefore:

• Gloria's rate of travel, x = 14 mph

,

• Jane's rate of travel = 4x = 4 x 14 =56 mph

Gloria's and Jane's rates of travel are 14 mph and 56 mph respectively.