Question

Starting at home, Jessica traveled uphill to the grocery store for 18 minutes at just 20 mph. She then traveled back home along the same path downhill at a speed of 60 mph.
What is her average speed for the entire trip from home to the grocery store and back?

Answer 1

Her average speed for the entire trip from home to the grocery store and back is 30 mph.

Step-by-step explanation:

It is given that,

Jessica travels uphill from home to the store at the speed of 20 mph in 18 minutes i.e., [3/10]hrs

So, the distance travelled by her for the uphill journey = speed * time = 20 * (3/10) = 6 miles

Also given that, she travels the same distance from the store back to home at a speed of 60 mph

∴ Time taken by her for the downhill journey = distance/speed = 6/60 = [1/10] hr

Now,

The total distance covered during the entire trip (uphill & downhill) = 6 + 6 = 12 miles

And,

The total time taken by Jessica for the entire trip = [3/10] + [1/10] = [4/10] = [2/5] hr

Thus,

Her average speed for the entire trip from home to the grocery store and back is,

= [Total Distance] / [Total Time]

= [12] / [2/5]

= 30 miles per hour

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Also View:

It took a car 6 hours to cover the distance between points A and B with the speed of 50mp/h. How long will it take a bus to cover the same distance, if it travels at 40mp/h?

Tracey ran to the top of a steep hill with an average pace of 6 miles per hour she took the exact same trail back down. to her relief the decend was much faster. the average speed rose to 14 miles per hour if entire journy took tracey 1 hour to complete and she did not stop anywhere what is the length of the trail in miles in miles one way.

Answer 2

We need to know the following to answer the distance-time-speed question:

• $\text {Distance} = \text {Time} \times \text {Speed}$

• $\text{Time} = \dfrac{\text{Distance} }{\text{Speed} }$
• $\text{Speed} = \dfrac{\text{Distance} }{\text{Time} }$

To find the average speed across a journey with different speed, we will also need to know:

• $\text{Average Speed} = \dfrac{\text{Total Distance} }{\text{Total Time} }$

Given (First part of the journey):

Time = 18 minutes

Speed = 20mph

1. Since the time is given in minutes and the speed in hour, we shall change the time to hour:

$18 \text { minutes} = \dfrac{18}{60} \text{ hour}$

$18 \text { minutes} = \dfrac{3}{10} \text{ hour}$

2. Then we shall find the distance covered in this part of the journey:

$\text {Distance} = \text {Time} \times \text {Speed}$

$\text {Distance} = \dfrac{3}{10} \times 20$

$\text {Distance} = 6 \text { miles}$

Given (2nd part of the journey):

Distance = 6 miles (both ways are of equal distance)

Speed = 60 mph

3. Find the time taken to cover the second part of the journey:

$\text{Time} = \dfrac{\text{Distance} }{\text{Speed} }$

$\text{Time} = \dfrac{6 }{60 }$

$\text{Time} = \dfrac{1 }{10} \text { hour}$

4. Now we can find the total distance and the total time taken for the journey:

$\text{Total Distance} = 6 + 6$

$\text{Total Distance} = 12 \text { miles}$

$\text{Total Time} = \dfrac{3}{10} + \dfrac{1}{10}$

$\text{Total Time} = \dfrac{4}{10}$

$\text{Total Time} = \dfrac{2}{5} \text{ hour}$

5. Finally, we can find the average speed of the journey:

$\text{Average Speed} = \dfrac{\text{Total Distance} }{\text{Total Time} }$

$\text{Average Speed } = \text {Total Distance} \div \text{Total Time}$

$\text{Average Speed } = 12 \div \dfrac{2}{5}$

$\text{Average Speed } = 12 \times \dfrac{5}{2}$

$\text{Average Speed } = 30 \text{ mph}$

Answer: Her average speed for the entire trip is 30mph