pgmat wrote:
One hour after Adrienne started walking the 60 miles from X to Y, James started walking from X to Y as well. Adrienne walks 3 miles per hour and James walks 1 mile per hour faster than Adrienne. How far from X will James be when he catches up to Adrienne?
A) 8 miles
B) 9 miles
C) 10 miles
D) 11 miles
E) 12 miles
Whats the best way to solve this problem? Is the distance from X to Y in the problem matter? Please give me detailed steps. Thank you.
This way looks time consuming. It isn't; took under a minute.
Travelers in same direction? B-->A-->
SUBTRACT rates. Use
\(\frac{D}{r}=t\) to find time taken to catch her. Finally, use time taken to find distance.
1. Find distance between them
Adrienne walked for one hour before James started. At 3 miles/hr * 1 hr, she walked 3 miles.
Three miles is the distance between them, the "gap."
2. Find combined or relative rate. This is a chase problem. They're walking in the
same direction, so
subtract their rates: (4-3) = 1 mi/hr
4. Find time for J to catch A from the distance and relative rate. D/r = t
At 1 mi/hr, for a distance of 3 miles it will take 3 mi/1 mph = 3 hours for him to catch her.
5. How far did James walk? rt= D
4 miles/hr * 3 hrs = 12 miles
Answer E
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