Exercise Module Performance Task Page 240

Jamal's times are represented in the table shown below.

Jamal's Race
Distance (mi)	Time (min)
4	26
8	56
12	90
16	128
20	170

Kendra's progress is shown as a scatter plot.

Comparing their data

In order to better compare the data, let's plot Jamal's times on a coordinate plane as well. We can connect the points with line segments to look at the general trend.

Notice that we cannot represent the points on the same line. The line is slightly bent. However, it continues at about the same average pace the whole time. Let's connect the points of the Kendra's graph and convert the time from hours to minutes in order to graph both data on the same coordinate plane.

Who will finish first?

Now, let's extend the graphs assuming that both runners will continue the same general trend line as for their first 20 miles. Then we can estimate which one of them will finish the race first.

As we can see from the graph, Jamal and Kendra maintain their average speeds during the race. Let's find their average speeds by using the following formula. distance=rate*time ⇒ d= r t Let's with Jamal's speed. According to his table, he runs 20 miles in 170 minutes.

d=rt

SubstituteII

d= 20, t= 170

20mi=r* 170 min

DivEqn

.LHS /170min.=.RHS /170min.

20mi/170 min=r

RearrangeEqn

Rearrange equation

r=20mi/170 min

HourToMin

1h=60 min

r=20mi/2.8 h

CalcQuot

Calculate quotient

r ≈ 7.1 mi/h

Jamal's speed is 7.1 miles per hour. Next, we will find Kendra's speed using her graph. She ran 16 miles in 2.5 hours.

d=rt

SubstituteII

d= 16, t= 2.5

16mi=r* 2.5 h

DivEqn

.LHS /2.5 h.=.RHS /2.5 h.

16mi/2.5 h=r

RearrangeEqn

Rearrange equation

r=16mi/2.5 h

CalcQuot

Calculate quotient

r ≈ 6.4 mi/h

Her speed is 6.4 miles per hour. Because we now know for certain that Jamal has a faster speed, we can conclude that Jamal will finish the race before Kendra.

The time difference

Now, let's use the same formula, using their average speeds and the total distance that they will run, to find their predicted running times. Jamal will run 26.2 miles with an average speed or 7.1 miles per hour.

d=rt

SubstituteII

d= 26.2, r= 7.1

26.2= 7.1* t

DivEqn

.LHS /7.1.=.RHS /7.1.

3.7≈ t

RearrangeEqn

Rearrange equation

t≈ 3.7

He will finish the race in approximately 3.7 hours. Let's find the Kendra's time.

d=rt