Can anyone help?

Question

1. Molly left home and drove toward the ferry office at an average speed of 27 mph. Mark left two hours later and drove in the same direction but with an average speed of 45 mph. How long did Molly drive before Mark caught up?

Answer 1

Hi April,

 

The key here is knowing that when Mark does catch up to Molly in t hours then each would have driven the same distance.  Therefore, we can write this equation to solve for Molly's drive time (t + 2) when Mark catches up to her:

    27(t + 2) = 45t

    27t + 54 = 45t

    45t - 27t = 54

    18t = 54

    t = 54/18

    t = 3 hours (Mark's drive time to catch-up)

    t + 2 = 3 +2

    t + 2 = 5 hours (Molly's drive time at catch-up)

 

We verify our answers by plugging them back into our equation to see that both distances prove equal:

    27(t + 2) = 45t

    27(5) = 45(3)

    135 miles = 135 miles (both distances are equal)

 

Since both distances are equal after plugging in our answers for both times, we know that our answers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.