Calculate the average speed

[chijioke]

The road from A to B is 10km uphill followed by 20km downhill. a motorcyclist averages 36km/hr uphill and 90km/hr downhill. Calculate the average speed (a) from A to B (b) from B to A?

At least I can solve the first part of the questions.

$$\text{Time uphill} =\frac{10}{36}~\text{hrs}$$$$\text{Time downhill} =\frac{20}{90}~\text{hrs}$$$$\text{Total time} =\frac{5}{18}+\frac{2}{9}=\frac{1}{2} ~\text{hrs}$$$$\text{Total distance} = 30 km$$$$\text{Avg speed} = \frac{30}{\frac{1}{2}} = 60~ km/hr$$I can solve the second part of the problem if I can the picture of the problem correctly. Is this the correct picture of the problem?

 

[Dr.Peterson]

The road from A to B is 10km uphill followed by 20km downhill. a motorcyclist averages 36km/hr uphill and 90km/hr downhill. Calculate the average speed (a) from A to B (b) from B to A?

At least I can solve the first part of the questions.

$$\text{Time uphill} =\frac{10}{36}~\text{hrs}$$$$\text{Time downhill} =\frac{20}{90}~\text{hrs}$$$$\text{Total time} =\frac{5}{18}+\frac{2}{9}=\frac{1}{2} ~\text{hrs}$$$$\text{Total distance} = 30 km$$$$\text{Avg speed} = \frac{30}{\frac{1}{2}} = 60~ km/hr$$I can solve the second part of the problem if I can the picture of the problem correctly. Is this the correct picture of the problem?
View attachment 37604

The picture is the same for both parts (except that you read it backward for the second). You got the first part right, so just do the second part and show your work again. You'll probably have it right.

 

[chijioke]

for the first part of the problem.


For the second part of the problem

Admin please help me make the pictures enter the op.

 

[Dr.Peterson]

In this modified picture, you have to interchange the words "uphill" and "downhill" for part B. What was uphill is now downhill.

 

[The Highlander]

Admin please help me make the pictures enter the op.

This diagram should work for both parts of the problem...

​

Hope that helps.

 

[Dr.Peterson]

I can solve the second part of the problem if I can the picture of the problem correctly. Is this the correct picture of the problem?

Yes, after the changes you made. Now show us your work, which, again, should be correct!

You may also want to consider, as a check, whether you expect the average speed to be more or less than in the first part, and why.

 

[chijioke]

Yes, after the changes you made. Now show us your work, which, again, should be correct!

This diagram should work for both parts of the problem...

View attachment 37607​

Hope that helps.

You may also want to consider, as a check, whether you expect the average speed to be more or less than in the first part, and why.

Calculation for average speed from B to A as
distance uphill = 20 km, speed uphill = 90 km/h
distance downhill =10km, speed downhill = 36 km/h
$$\text{time down hill}=\frac{10}{90}=\frac{1}{9}~hr$$$$\text{time up hill}=\frac{20}{36}=\frac{5}{9}~hr$$$$\text{total time}=\frac{1}{9}+\frac{5}{9}=\frac{6}{9}=\frac{2}{3}=~hr$$$$\text{average speed}=\frac{30}{1} \times \frac{3}{2}= 45km/h$$

 

[Dr.Peterson]

Clearly you meant to say this:

Calculation for average speed from B to A as
distance uphill = 20 km, speed uphill = 36 km/h
distance downhill =10km, speed downhill = 90 km/h

Your answer is correct.

And, as you should expect, the average speed is less than from A to B, because more time is spent at the slower speed.