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Chapter 7: Q.290 (page 716)

Laney wanted to lose some weight so she planned a day of exercising. She spent a total of 2 hours riding her bike and jogging. She biked for 12 miles and jogged for 6 miles. Her rate for jogging was 10 mph less than biking rate. What was her rate when jogging?

Short Answer

Expert verified

The jogging rate is 5 mph .

Step by step solution

01

Step 1. Given Information.

Total of 2 hours riding her bike and jogging.

She biked for 12 miles and jogged for 6 miles.

The rate for jogging was 10 mph less than biking rate.

02

. Equations for Ratio and Proportion

Let rate of jogging be x mph .

The formula for speed is:-

Speed=DistanceTimeTime=DistanceSpeed

Time taken in biking =12x

Time taken in jogging =6x-10

Since , Total time is 2 hours.

Therefore, The equation is :-

12x+6x-10=2

03

. Solving the Proportional equation .

Solving the equation:-

12x+6x-10=26x+3x-10=16(x-10)+3x=1x(x-10)6x-60+3x=x2-10xx2-19x+60=0

Solving quadratic equation by factorization , we get:-

x2-15x-4x+60=0x(x-15)-4(x-15)=0(x-15)(x-4)=0x=15;x=4

Since , For the value of x the jogging speed will become negative. Therefore, negative speed does not makes sense.

Hence, The jogging rate is 5 mph .

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