I'm just curious if you would use the same formula for this problem as any other speed problem. Distance traveled/time elapsed Time = distance/speed

Question: Sheerwood is a bicyclist. He makes a daily ride of 40mph at a constant speed. If he trains hard, he can increase his speed by 4 mph, which would result in a half-hour decrease in time. Find his new speed.

40mph/4mph ? 10mph

You said he travels at 40 mph. If he increases his speed by 4 mph he is going 44 mph.

I assume you mean he pedals 40 miles, not 40 mph?

Going with that:

Let his original rate be rt=40... [1]

He increases his speed by 4 and his time decreases by 1/2 hr.

(r+4)(t-1/2)=40... [2]

From [1], we see that t=40/r

Sub into [2]:

(r+4)((40/r)-1/2)=40

Solve for r (his original speed). You can easily find his new speed by just adding 4.

I think you have made an error: It should be 40 miles, not 40 mph

You have to start with:

Let original speed = x

New speed = x + 4

Time taken with original speed = 40/x

Time taken with new speed = 40/(x+4)

Hence:

40/x - 40/(x+4) = .5 (30 min = .5 hours)

Solve this equation

If the speed traveled was 40 MPH for 5 hours, he would travel 200 miles per day.

If the speed traveled was 44 MPH for 4.5 hours, he would travel 198 miles per day.

Your pseudo formula stated he could increase 4 MPH making it an average of 44 MPH to answer your last statement.

I should not even be helping here but what do you math guys think of the above in the travel speed was actually 40 MPH. Then knocking off a half an hour to go the same distance (approx) at 44 MPH.

I could see someone training for 5 hours a day and travelling 200 miles.

speed = distance/time

Otoy lhat ng answers niyo nu!!