Question

Isaac trained for 4 hours yesterday. He ran 10 miles and then biked 15 miles. His biking speed is 6 mph faster than his running speed. What is his running speed?

Answer 1

Let:

x = biking speed

y = running speed

To solve this question, follow the steps below.

Step 01: Write an equation that relates the running and biking speed.

Given: His biking speed is 6 mph faster than his running speed

Then,

x = y + 6

Step 02: Write an equation to the total hours trained.

Given: speed = distance/time

Then, time = distance/speed

4 hours = (distance/speed)biking + ((distance/speed)running

Then,

4 = 15/x + 10/y

Step 03: Substitute x by (y + 6) in the equation from step 02.

`\begin{gathered} 4=(15)/(x)+(10)/(y) \\ 4=(15)/(y+6)+(10)/(y) \end{gathered}`

Step 04: Solve the equation above.

`\begin{gathered} (4\left(y+6\right)\left(y\right)=15y+10(y+6))/((y+6)(y)) \\ \begin{equation*} 4\left(y+6\right)\left(y\right)=15y+10(y+6) \end{equation*} \\ (4y+24)y=15y+10y+60 \\ 4y^2+24y=25y+60 \\ 4y^2+24y-25y-60=0 \\ 4y-y-60=0 \end{gathered}`

Use the quadratic formula to solve the equation. For a equation ax² + bx+ c = 0, the roots are:

`x=(-b\pm√(b^2-4ac))/(2a)`

Then, substituting the values from this question:

Since y must be positive, y = 4 mph.

Step 06: Find x.

x = y + 6

`\begin{gathered} x=4+6 \\ x=10mph \end{gathered}`

Since y = running speed:

Answer: the running speed was 4 mph.