Shanice's car is traveling 10 miles per hour slower than twice the speed of Brandon's car. She covers 93 miles in 1 hour 30 minutes. How fast is Brandon driving?
The speed of a body is the distance it travels per unit of time. That means that we can also find out how far an
object moves in a certain amount of time if we know its speed: we use the equation "distance = speed time."
Here, we don't know either Brandon's speed or Shanice's, but since the question asks for Brandon's speed, that's what we'll use as our variable x.
The distance Shanice covers in miles is 93, and the time in hours is 1.5. Her speed is 10 less than twice Brandon's speed.
Shanice's speed is:
x - 10 miles per hour.
Substituting into the equation distance = speed × time gives us
93 = ( x - 10)1.5
First we distribute, to get
93 = 3x -
Then we add 15 to both sides to get
108 = 3x.
Finally we divide by 3 to get
= x.
Brandon is driving at miles per hour.
Check: We can check this answer by considering the situation another way: we can solve for Shanice's speed instead of Brandon's and then check that against Brandon's speed.
The equation for Shanice's speed is simply 2x - 10 = 2(
-10
72 - 10 = 62
So, Shanice is traveling at
miles per hour.
The problem tells us that Shanice is traveling 10 mph slower than twice Brandon's speed;
that would mean that 62 is equal to 2 times 36 minus 10. Is that true? Well, 2 times 36 is 72, minus 10 is 62.