Chapter 3.3, Problem 51PPS

(a)

To determine

Create a table to show how far Ma and Mi can travel walking and riding their bikes .Including distances for 0,1,2,3,and 4 hours.

Explanation of Solution

Given:

Ma and Mi can walk 3.5 miles per hour and ride their bikes 10 miles per hour.

Calculation:

Given:

  $v_{walking}=3.5\text{ miles per hour}$

  $v_{riding}=10\text{ miles per hour}$

Make a table:

Distance = (speed)(time)

Time(hours)	Distance(in miles)(walking)	Distance(in miles)(riding bike)
0	$3.5(0)=0$	$10(0)=0$
1	$3.5(1)=3.5$	$10(1)=10$
2	$3.5(2)=7$	$10(2)=20$
3	$3.5(3)=10.5$	$10(3)=30$
4	$3.5(4)=14$	$10(4)=40$

(b)

To determine

Create a graph to show how far Ma and Mi can travel based on time for both walking and riding their bikes.

Explanation of Solution

Given:

Ma and Mi can walk 3.5 miles per hour and ride their bikes 10 miles per hour.

Calculation:

From part (a),

Time(hours)	Distance(in miles)(walking)	Distance(in miles)(riding bike)
0	$3.5(0)=0$	$10(0)=0$
1	$3.5(1)=3.5$	$10(1)=10$
2	$3.5(2)=7$	$10(2)=20$
3	$3.5(3)=10.5$	$10(3)=30$
4	$3.5(4)=14$	$10(4)=40$

Now represent the data on the axis :

  

(c)

To determine

What does the slope represent in the graph.

Answer to Problem 51PPS

Speed(miles/hour)

Explanation of Solution

Given:

Ma and Mi can walk 3.5 miles per hour and ride their bikes 10 miles per hour.

Calculation:

From part (b) , the slope represents $\frac{y-axis}{x-axis}=\frac{miles}{hour}=speed$

So, slope represents speed in miles/hour.

(d)

To determine

Ma’s mom says they can only go if they can make it to the music store and back in less than two hours.If they want to spend at least 30 minutes in the music store and it is four miles away, can they make it .Should they walk or ride their bikes.

Answer to Problem 51PPS

48 minutes , they will ride their bikes.

Explanation of Solution

Given:

Ma and Mi can walk 3.5 miles per hour and ride their bikes 10 miles per hour.

Calculation:

The music store is 4 miles away.

So, the total distance they have to travel to go and come back from store = 4 + 4 =8 miles.

The time they have for travelling to the store and come back = $2-\frac{30}{60}=2-0.5=1.5$ hours, since their mom allows total of 2 hours and they need to spend 30 minutes at the store.

So, the speed they need = $\frac{\text{distance}}{time}=\frac{8}{1.5}\approx 5.33\text{ miles/hour}$

Also,

  $v_{walking}=3.5\text{ miles per hour}$

  $v_{riding}=10\text{ miles per hour}$

Since the speed needed is more than the walking speed , they must take the bikes.

So, time taken = $\frac{\text{distance}}{speed}=\frac{8}{10}=\frac{4}{5}\cdot 60=48\text{ minutes}\mathrm{..........}\text{[1 hour = 60 minutes]}$