gmattesttaker2 wrote:
Paul and Mary start getting away from each other from the same point along a straight line.
Paul travels at 4 mph while Mary travels at 5 mph. If Mary started travelling one hour later, how long will it take them to be 40 miles apart?

gmattesttaker2 wrote:Hello,

Can you please assist with this :

Paul and Mary start getting away from each other from the same point along a straight line.
Paul travels at 4 mph while Mary travels at 5 mph. If Mary started travelling one hour later, how long will it take them to be 40 miles apart?

My approach was as follows:

Rate x Time = Distance

Paul: 4 x t = 4t
Mary: 5 x (t-1) = 5(t-1)

So, 4t + 5(t-1) = 40
=> 4t + 5t - 5 = 40
=> 9t = 45
=> t = 5

At this point, you are done
t = 5, which means it takes 5 hours for the two people to be 40 miles apart.
DONE!

I was thinking something on these lines:

This next part proves that your answer is correct
4 x 5 = 20 (so Paul's total distance traveled = 20 miles)
and 5 x (5-1) = 20 (so Mary's total distance traveled = 20 miles)
Since both people traveled 20 miles, they are 40 miles apart . . . Perfect!


So, t = 9 hours No. All this means is that Paul traveled for 5 hours and Mary traveled for 4 hours. We get a total of 9 hours, but the question doesn't ask us to find the sum of the travel times