BrentGMATPrepNow
On a 330-mile road trip, Kyle drove at a constant speed of 60 miles per hour for the first part of the trip, and then he drove at a constant speed of 40 miles per hour for the remainder of the trip. If Kyle spent 3 hours longer driving 60 miles per hour than he spent driving 40 miles per hour, how many hours did it take Kyle to complete the 330-mile trip?
A) 5
B) 5.5
C) 6
D) 6.5
E) 7
First recognize that Kyle's trip consists of two parts:
1) the part where Kyle drives at 60 mph
2) the part where Kyle drives at 40 mph
Let's start by writing a couple of "word equations" that consist of those two parts.
One possible word equation is:
(distance driven at 60 mph) + (distance driven at 40 mph) = 330 miles (since the entire trip is 330 miles)Another possible word equation is:
(time spent driving at 60 mph) - (time spent driving at 40 mph) = 3 hours (since Kyle drives at 60 mph for 3 hours longer he drives at 40 mph)Either of these word equations will help us arrive at the correct answer. Let's do both for "fun."
SOLUTION #1: Using
(distance driven at 60 mph) + (distance driven at 40 mph) = 330 miles (since the entire trip is 330)Distance = (rate)(time)We know Kyle's speed for both parts of the trip, but we don't know his travel time for each part of the trip.
So, let's let t = the amount of time Kyle spent driving at 40 mph
This means t + 3 = the amount of time Kyle spent driving at 60 mph
(since Kyle spent 3 hours longer driving at 60 mph)We can now substitute the following values into our word equation:
(60)(t + 3) + (40)(t) = 330Expand: 60t + 180 + 40t = 330
Simplify: 100t + 180 = 330
Subtract 180 from both sides of the equation: 100t = 150
Solve: t = 150/100 = 1.5
This means Kyle spent
1.5 hours driving at a speed of 40 mph
Since t + 3 = the time Kyle's spent driving at 60 mph, we can conclude that Kyle spent
4.5 hours driving at a speed of 60 mph
So, Kyle's total travel time =
1.5 hours + 4.5 hours = 6 hoursAnswer: C
SOLUTION #2: Using
(time spent driving at 60 mph) - (time spent driving at 40 mph) = 3 hourstime= distance/ rateWe know Kyle's rate for both parts of the trip, but we don't know the distance he travelled for each part of the trip.
So, let's let d = the distance Kyle drove at 60 mph
This means 330 - d =the distance Kyle drove at at 40 mph
(since Kyle drove a total distance of 330 miles)We can now substitute the following values into our word equation:
d/60 - (330 - d)/40 = 3 hoursTo eliminate the fractions will multiply both sides of the equation by 120 (the least common multiple of 60 and 40)
When we do this we get: 2d - 3(330 - d) = 360
Expand: 2d - 990 + 3d = 360
Simplify: 5d - 990 = 360
Add 990 to both sides: 5d = 1350
Solve: d = 1350/5 = 270
This means Kyle drove 270 miles at 60 mph, which means he drove the remaining 60 miles at 40 mph
To calculate the total driving time, we'll use time = distance/rate
So, the total driving time = 270/6 + 60/40
= 4.5 + 1.5
= 6 hours
Answer: C