i am having a hard time with this one

Question

 at 1 pm, Harvey leaves his house in Pittsburgh, heading east toward Philadelphia, traveling at 70 mph. At 2:15pm, his brother leaves his house in Harrisburg, which is 150 miles closer, and also travels to Philadelphia. If his brother travels at 55 mph, at what time will Harvey pass his brother

Answer 1

distance = rate x time

 

The race on I-76 begins at 1 PM with Harvey.

 

1 hour and 15 minutes later, or 1.25 hours later, the brother

joins the race.

 

The brother travels  d = 55 * t  where t is the time they meet.

 

Harvey travels  d + 150 = 70 * (t + 1.25) <-- 150 miles more and 1.25 hours longer

 

Substituting the first equation into the second:

 

 55t + 150 = 70(t +1.25)

 

 55t + 150 = 70t + 87.5

 

0 = 70t + 87.5 - 150 - 55t

 

0 = 15t - 62.5

 

t = 62.5/15 = 625/150 = 25/6 = 4 hours and 10 minutes

 

The brother leaves Harrisburgh at 2:15 pm and travels 55 * 25/6 = 229 and 1/6 miles

Harvey leaves Pittsburgh at 1 pm and travels 70*(25/6+1.25) = 379 and 1/6 miles.

Notice the difference between these distances is exactly 150 miles.

 

As a double check. notice that

Harvey will have been on the road for 5 hours and 25 minutes.

At 70 mph, that's 379 and 1/6 miles.

 

The brother will have been on the road for 4 hours and 10 minutes.

At 55 mph, that's 229 and 1/6 miles.

 

These same distances result in the same difference of 150 miles.

 

The answer is 2:15 pm + 4 hours and 10 minutes . 

So they will meet at 6:25 pm