Question

Marta,Loribeth,and Ira all have bicycles.The table shows the number of miles of each rider's last bike ride, as well as the time it took each rider to complete the ride.
Distance of last ride (in miles) Time spent on last bike ride (in minutes)

Marta 8 80

Loribeth 6 42

Ira 15 75


If all three riders travel for 3.5 hours at the same speed as their last ride,how many total miles will the three riders travel altogether ? Explain.

Answer 1

We have been given a table of data that represents the distances traveled by three bicycle riders and time spent on their rides.

To find sum of distances traveled by three riders at the same rate, we will have to find unit rate at which each rider is cycling.

$\text{Rate at which Marta is cycling}=\frac{8\text{ miles}}{80\text{ minutes}}$

$\text{Rate at which Marta is cycling}=0.1\frac{\text{ miles}}{\text{ minute}}$

Let us find Loribeth's unit rate of cycling.

$\text{Rate at which Loribeth is cycling}=\frac{6\text{ miles}}{42\text{ minutes}}$

$\text{Rate at which Loribeth is cycling}=0.1428571428571429\frac{\text{ miles}}{\text{ minute}}$

Let us find Ira's unit rate of cycling.

$\text{Rate at which Ira is cycling}=\frac{15\text{ miles}}{75\text{ minutes}}$

$\text{Rate at which Ira is cycling}=0.2\frac{\text{ miles}}{\text{ minute}}$

Let us convert 3.5 hours in minutes.

3.5 hours = 3 hours+50 minutes=(3*60+50) minutes =230 minutes.

Now let us add rates of our three cycles and then multiply the sum by 230 minutes to find distance traveled by three riders altogether.

$\text{Distance traveled by three riders altogether}=230\cdot(0.1+0.2+0.1428571428571429)$

$\text{Distance traveled by three riders altogether}=230\cdot(0.4428571428571429)$

$\text{Distance traveled by three riders altogether}=101.857$

Therefore, three riders will travel 101.857 miles while travelling altogether.

Answer 2

Answer:

The three riders travel 93 miles altogether.

Step-by-step explanation:

From the given table we will find the speed of each riders individually.

Speed = $\frac{distance}{time}$

Speed of Marta = $\frac{8}{80}$ = $\frac{1}{10}$ = 0.1 miles / min.

Speed of Loribeth = $\frac{6}{42}$ = $\frac{1}{7}$ = 0.143 miles/min.

Speed of Ira =  $\frac{15}{75}$ = $\frac{1}{5}$ = 0.2 miles / min.

Now we will calculate the distance covered by each riders with their individual speed in 3.5 hours

Since 3.5 hours = 3 × 60 + 30 = 180 + 30 = 210 minutes

Therefore, distance covered by Marta = speed × time.

                                                               = 0.1 × 210 = 21 miles

Distance covered by Loribeth = 0.143 × 210 = 30 miles

Distance covered by Ira = 0.2 × 210 = 42 miles

Therefore, total distance covered by all = 21 + 30 + 42 = 93 miles.

The three riders travel 93 miles altogether.