The sum of the rates is (30 mi)/(3/5 hr) = 50 mph.

The difference of the rates is (30 mi)/(5/6 hr) = 36 mph.

Suppose p is the speed of the plane and w is the speed of the wind.

(p + w) + (p - w) = sum + difference

2p = sum + difference

(p + w) - (p - w) = sum - difference

2w = sum - difference

It is useful to remember this solution to sum and difference problems, as you are likely to see a lot of algebra problems that can make use of it.

The difference of the rates is (30 mi)/(5/6 hr) = 36 mph.

**The plane's speed is the average of these: (50 mph + 36 mph)/2 = 43 mph****The wind's speed is half the difference of these: (50 mph - 36 mph)/2 = 7 mph**Suppose p is the speed of the plane and w is the speed of the wind.

**p + w = sum****p - w = difference**Add these two equations to get(p + w) + (p - w) = sum + difference

2p = sum + difference

**p = (sum + difference)/2**Subtract the second equation from the first to get(p + w) - (p - w) = sum - difference

2w = sum - difference

**w = (sum - difference)/2**It is useful to remember this solution to sum and difference problems, as you are likely to see a lot of algebra problems that can make use of it.