Can someone help me with this problem?

[03]

Let the distance be 60 miles

Time taken for going is 60/60=1 hr

Time taken for returning is 60/30=2 hrs

Total distance=120 miles

Total time taken=3 hrs

Average speed=120/3=40 mph

The distance has been taken as 60 miles as it is the LCM of both the speeds i.e 60 and 30 mph.We may solve the problem by taking the distance as 1 mile or x mile but that will involve fractions and hence is avoided

No it isn't. Let's say that it took x hours to drive y miles at 60 mph.

Speed = distance/time = y/x = 60

Now, on the way back, the distance hasn't changed, but the speed has, so the time must also have changed. So:

time = distance/speed = y/30

Since the original time taken was x, we can rearrange the first expression to give x:

x = y/60

Notice how the new time is y/30, which is actually double y/60

So the time on the way back is 2x

Now that we know the total time taken was 2x + x = 3x, and the total distance was y + y = 2y

So the average speed = total distance/total time.

Average speed = 2y/3x, which is 2/3 times y/x, and we know from the beginning that y/x = 60, So the average speed was 2/3 times 60.

So average speed = 40mph

Hope that's not too confusing.

Right, because you spend twice as long at 30 mph than you do at 60 mph.

So, let's say it takes you 1 hour to go at 60 mph. It would take you 2 hours to go at 30 mph. That means it took you 3 hours to go 120 miles total. That's 120/3 = 40 miles per hour.

A general equation would be to say that you spent 1 unit of time at 60mph and 2 units at 30mph.

The average would be:

(1*60 + 2*30)/(1+2)

(60 + 60)(3)

120/3

40mph again.

Let's say it is 120 miles to your Mom's house

Then it would take 2 hours to get there and 4 hours to get back . So you traveled 240 miles in 6hours for an average speed of 240/6 = 40 mph

average speed = total distance / total time

since it is a round trip, the total distance is 2x

the time it takes to go to you mom's house is x/60

the time it takes to go back is x/30

the total time is x/60 + x/30 = (30x + 60x)/1800 = x/20

so averg. speed = 2x / (x/20) = 2x * 20/x = 40 mi/hr <== ans