A jogger ran 8 miles and then walked 6 miles. The jogger's running speed was 5 miles per hour faster than her walking speed. The total time for jogging and walking was 2 hours. What was the jogger's walking speed and jogging speed?

1 Answer
Mar 26, 2018

S_r=10mph
S_w=5mph

Explanation:

Let 'r' denote running and 'w' denote walking.
Let D be distance travelled. So,
(D_r)=8mi
(D_w)=6mi

Let "S" be the speed. So,
And since speed of running is 5mph faster than walking. So,
(S_r)=S_w + 5mph

Let T be the time.So,
Total time taken is 2 hrs.
Since the time includes T_r and T_w. We could say,
(T_r)+(T_w)=2
or, (T_r)=2-(T_w)

We know,
S = (DeltaD)/(Deltat)
(S_r)=8/(2-T_w) and
(S_w)=6/(T_w)

As mentioned
(S_r)=(S_w)+5mph
or, 8/(2-T_w)=5+6/(T_w)
For sake of ease let's suppose (T_w)=x
So,
8/(2-x)=5+6/x
or, 8/(2-x)=(5x+6)/x
Cross multiplying,
or, 8x=(5x+6)(2-x)
or, 8x=4x-(5x^2)+12
or, 8x-4x+(5x^2)-12=0
or, (5x^2)+4x-12=0
Factorization by splitting the middle term,
or, (5x^2)+(10-6)x-12=0
or, (5x^2)+10x-6x-12=0
or, 5x (x+2)-6 (x+2)=0
Use reverse of distributive property.
or, (5x-6)(x+2)=0

Since time is positive we must choose such binomial from above that yields positive value.
Choose
(5x-6)=0
x=6/5
x=(T_w)=6/5hrs

So,
S_w=(deltaD_w)/(deltaT_w)
=6/(6/5)
=30/6
=5 mph

Again S_r=5mph+S_w
=5mph+5mph
=10mph

:.S_r=10mph
:.S_w=5mph