A town N is 340 km due west of town G and town K is west of town N. A helicopter Zebra left G for K at 9.00 a.m. Another helicopter Buffalo left N for K at 11.00 a.m. Helicopter Buffalo traveled at an average speed of 20 km/h faster than Zebra. If both helicopters reached K at 12.30 pm find the speed of helicopter Buffalo.
To find the speed of helicopter Buffalo, let's break down the problem and use the information given.
1. Town N is 340 km due west of town G, meaning the distance between N and G is 340 km.
2. Town K is west of town N, but we don't know the exact distance between N and K.
3. Helicopter Zebra left G for K at 9.00 a.m., and helicopter Buffalo left N for K at 11.00 a.m.
4. Both helicopters reached K at 12.30 p.m., meaning they traveled for 3.5 hours.
Now, let's calculate the speed of helicopter Buffalo.
Let's assume the speed of helicopter Zebra is "x" km/h.
Since helicopter Buffalo traveled at an average speed of 20 km/h faster than Zebra, the speed of helicopter Buffalo would be "x + 20" km/h.
Now, let's calculate the distance traveled by each helicopter.
Distance traveled by helicopter Zebra:
Distance = Speed × Time
Distance = x km/h × 3.5 hours
Distance traveled by helicopter Buffalo:
Distance = Speed × Time
Distance = (x + 20) km/h × 1.5 hours
Since both helicopters reached town K, the sum of their distances should be equal to the distance between N and K.
Distance traveled by helicopter Zebra + Distance traveled by helicopter Buffalo = Distance between N and K
(x km/h × 3.5 hours) + ((x + 20) km/h × 1.5 hours) = Distance between N and K
Now, we can use the information given in the problem to solve for x, the speed of helicopter Buffalo.
Distance between N and K = 340 km
(3.5x) + (1.5(x + 20)) = 340
Simplifying the equation:
3.5x + 1.5x + 30 = 340
5x + 30 = 340
5x = 310
x = 62
Hence, the speed of helicopter Buffalo (x + 20) would be:
62 km/h + 20 km/h = 82 km/h
Therefore, the speed of helicopter Buffalo is 82 km/h.