Distance Problem

Question

On his way to visit soren, peter averaged 7mi/h on his skateboard and 4 mi/h walking. If soren lives 6 miles away and the whole trip took 1 h, how many miles did Peter travel by skateboard? (Hint: First find the two times)

Answer 1

Let x = distance traveled by skateboard

 

Then 6-x = distance traveled by foot

 

Distance = (Rate)(Time), so Time = (Distance)/(Rate)

 

Total time = 1

 

So, time on skateboard + time walking = 1

 

Thus, x/7 + (6-x)/4 = 1

 

Multiply the equation by the LCD, 28:

 

   4x + 7(6-x) = 28

 

   4x + 42 - 7x = 28

 

               -3x = -14

 

                  x = 14/3 miles = 4 2/3 miles

 

 

Answer 2

Skateboard speed and time:  v₁ = 7 mi/h, t₁ = ?

 

Walking speed and time:  v₂ = 4 mi/h, t₂ = ?

 

Total distance traveled:  v₁t₁ + v₂t₂ = 7t₁ + 4t₂ = 6 mi

 

Total time:  T = t₁ + t₂ = 1 h

 

Solve the system of equations 

 

(i)  7t₁ + 4t₂ = 6

(ii) t₁ + t₂ = 1

 

From (ii) get t₁ = 1 - t₂ and substitute into (i) to find t₂:

 

7(1 - t₂) + 4t₂ = 6

-3t₂ = -1

t₂ = 1/3 h

 

Then

 

t₁ = 1 - t₂ = (1 - 1/3) h = 2/3 h

 

Distance traveled by skateboard:

 

d₁ = v₁t₁ = 7(2/3) mi ≅ 4.67 mi