GMATPrepNow wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?
A) 7.5
B) 10
C) 12
D) 12.5
E) 15
As I mention in the video below, these kinds of questions can be solved in a variety of ways.
For our 3rd approach, let's start with a word equation involving distances traveled.
Since Bill and Ted both traveled 240 miles, we can write:
Bill's travel distance = Ted's travel distance Let
x = Bill's speed
So,
x + 5 = Ted's speed
Let
t = Ted's travel time (in hours)
So,
t + 4 = = Bill's travel time (in hours)
Distance = (speed)(time)Plug values into the word equation to get: (
x)(
t + 4) = (
x + 5)(
t)
Expand to get: xt + 4x = xt + 5t
Subtract xt from both sides to get: 4x = 5t
Divide both sides by 5 to get:
4x/5 = tWhere do we go from here?
Well, we know that Bill traveled 240 miles
So, (Bill's speed)(Bill's travel time) = 240
In other words: (
x)(
t + 4) = 240
Replace
t with
4x/5 to get: (x)(4x/5 + 4) = 240
Expand: 4x²/5 + 4x = 240
Multiply both sides by 5 to get: 4x² + 20x = 1200
Divide both sides by 4 to get: x² + 5x = 300
Rewrite as: x² + 5x - 300 = 0
Factor: (x - 15)(x + 20) = 0
So, EITHER x = 15 OR x = -20
Since the speed cannot be negative, it must be the case that x = 15
Answer: 15
RELATED VIDEO FROM OUR COURSE