Find the miles per hour answer(Rationals)

Question

Sally was able to drive an average of 40 miles per hour faster in her car after the traffic cleared. She drove 18 miles in traffic before it cleared and then drove another 116 miles. If the total trip took 3 hours, then what was her average speed in traffic?

Answer 1

d = r · t

 

d₁ = r₁ · t/

18/r₁ = t₁

 

d₂ = r₂ · t

116 = (r₁ + 40)t

116/(r₁ + 40) = t₂

 

t₁ + t₂ = 3

18/r₁ + 116/(r₁ + 40) = 3

 

Can you solve for r₁? Then calculate average speed.

Answer 2

We need to make use of the formula:

 

distance = rate x time

 

In traffic, let's call Sally's rate x, and we know she traveled a distance of 18 mi.

 

Once traffic cleared, her rate is (x + 40), and we know that Sally traveled 116 mi. 

 

If she traveled a total of 3 hours, then the time she traveled in traffic can be y, and her time once traffic cleared can be 3 - y.

 

We now have two equations using the formula for distance traveled:

 

18 = x * y = xy

 

116 = (x + 40)(3 - y)

 

We can solve the first equation for y

 

y = 18/x

 

Plug this into the second equation

 

116 = (x + 40) (3 - 18/x)

 

116 = 3x - 18 + 120 - 720/x

 

116 = 3x - 720/x + 102

 

14 = 3x - 720/x

 

Multiply both sides by x to clear the fraction

 

14x = 3x² - 720

 

3x² - 14x - 720 = (3x + 40)(x - 18) = 0

 

We can eliminate the first factor of (3x + 40) because time cannot be negative

 

We now have x - 18 = 0 , or x = 18

 

Sally's average speed in traffic is 18 mi/hr