Question

Ken and Joe leave their apartment to go to a football game 60 miles away. Ken drives his car 40 mph faster than Joe can ride his bike. If it takes Joe 2 hours longer than Ken to get to the game, what is Joes speed in miles per hour

Answer 1

Yes I did tho wyeiwtw it is a little too old

Answer 2

Given:

Total distance = 60miles

Ken speed 40 mph faster than Joe.

Joe take 2 hours longer than Ken.

Find-:

Joes speed

Sol:

Formula of speed is:

`\text{ Speed = }\frac{\text{ Distance}}{\text{ Time}}`

Let Joe's speed is "x"

Then Ken's speed is "x+40"

Let Ken take time is "t"

Then Joe takes time is "t+2"

For Joe's speed:

`\begin{gathered} \text{ Speed = }x \\ \\ \text{ Time = }t+2 \end{gathered}`

So, speed is:

`\begin{gathered} \text{ Speed = }\frac{\text{ Distance}}{\text{ Time}} \\ \\ x=(60)/(t+2).................(1) \\ \\ \end{gathered}`

For Ken's speed:

`\begin{gathered} \text{ Speed = }x+40 \\ \\ \text{ Time = }t \end{gathered}`

So, speed is:

`\begin{gathered} \text{ Speed =}\frac{\text{ Distance}}{\text{ Time}} \\ \\ x+40=(60)/(t) \\ \\ t=(60)/(x+40)..............................(2) \end{gathered}`

From eq(2) put the value of "t" in eq(1) then:

`\begin{gathered} x=(60)/(t+2) \\ \\ t+2=(60)/(x) \\ \\ t=(60)/(x)-2 \\ \\ (60)/(x+40)=(60)/(x)-2 \end{gathered}`

Then, solve for "x"

`\begin{gathered} (60)/(x+40)=(60)/(x)-2 \\ \\ (60)/(x+40)=(60-2x)/(x) \\ \\ 60x=(x+40)(60-2x) \\ \\ 60x=60x-2x^2+2400-80x \\ \\ 2x^2+80x-2400=0 \\ \\ x^2+40x-1200=0 \end{gathered}`

Solve the quadratic equation then:

`\begin{gathered} x^2+40x-1200=0 \\ \\ x^2+60x-20x-1200=0 \\ \\ x(x+60)-20(x+60)=0 \\ \\ (x+60)(x-20)=0 \\ \\ x=-60,20 \end{gathered}`

Negative speed not possible so Joe speed is 20 mph