our man Ostap was going hame from kiev. He rod halfway-fifteen times as fast as he goes on foot. The second half he went by ox team. He can walk twice as fast as that. Would he have saved time if he had gone all the way on foot?

He ran halfway, fifteen times faster than walking. So he got there T/30 where T is the total walking time.

The second half, he walked, and it took 2*T/2 or T minues.

Total time: T+ T/30
Well, if he had walked it would have taken him only time T.

Yes.

Compare the time D/V to the time
(D/2)/2V + (D/2)/(V/2)= D/4V + D/V

To determine whether Ostap would have saved time if he had gone all the way on foot, we need to compare the time it took him to ride halfway and the time it would have taken him to walk the entire distance.

Let's assign some variables to the given information:
- Let's say the distance from Kiev to Ostap's destination is "D."
- Ostap's walking speed is "W" (in distance units per time unit).
- Ostap's riding speed is "R" (in distance units per time unit).
- Ostap's ox team speed is "O" (in distance units per time unit).

According to the given information:
- Ostap rode halfway-fifteen times as fast as he walks. Therefore, R = 15W.
- Ostap walks twice as fast as the ox team. Therefore, W = 2O.

Now, let's calculate the time it took him to ride halfway, and the time it would have taken him to walk the entire distance:

Time for riding halfway:
- Distance covered = D/2
- Time = Distance / Speed = (D/2) / R = (D/2) / (15W) = (D/2) / (15 * 2O) = D / (2 * 15 * 2O) = D / (60O)

Time for walking the entire distance:
- Distance covered = D
- Time = Distance / Speed = D / W

Now, let's substitute the given relation between speeds (W = 2O) and find out if walking the entire distance would be faster:

Time for riding halfway: D / (60O)
Time for walking the entire distance: D / W = D / (2O)

To compare the two times, we need to find the relationship between O and 1/60O:

60 / O = 1 / (1/60O) = 1 / (60O) * 60

Simplifying, we get:

60 / O = 1 / (60O) * 60
60 / O = 1

Therefore, O = 60.

Now we can substitute this value of O back into the time equations:

Time for riding halfway: D / (60O) = D / (60 * 60) = D / 3600
Time for walking the entire distance: D / W = D / (2O) = D / (2 * 60) = D / 120

Comparing the two times, we can see that D / 3600 is greater than D / 120.

Therefore, Ostap would have saved time if he had gone all the way on foot.