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.
If KN=x, and Z has speed b-20
Z flew for 3.5 hr
B flew for 1.5 hr
(b-20)(3.5) = 340+x
b(1.5) = x
(b-20)(3.5) = 340+b(1.5)
2b = 340+70
b = 205
check:
K is 307.5 KM west of N
So, K is 647.5 km west of G
647.5/185 = 3.5
307.5/205 = 1.5
To find the speed of helicopter Buffalo, we can follow these steps:
Step 1: Determine the time taken by helicopter Zebra to reach town K.
We know that both helicopters reached K at 12.30 pm, and helicopter Zebra left G at 9.00 am. So the time taken by Zebra is:
12.30 pm - 9.00 am = 3 hours and 30 minutes = 3.5 hours.
Step 2: Determine the time taken by helicopter Buffalo to reach town K.
Buffalo left N at 11.00 am and reached K at 12.30 pm. So the time taken by Buffalo is:
12.30 pm - 11.00 am = 1 hour and 30 minutes = 1.5 hours.
Step 3: Calculate the distance traveled by each helicopter.
To find the distance traveled by Zebra, we can use the formula:
Distance = Speed × Time
Since Zebra traveled from G to K, and the distance between G and K is 340 km, we have:
Distance_Zebra = Speed_Zebra × Time_Zebra
Distance_Zebra = Speed_Zebra × 3.5 (hours)
To find the distance traveled by Buffalo, we have:
Distance_Buffalo = Speed_Buffalo × Time_Buffalo
Distance_Buffalo = Speed_Buffalo × 1.5 (hours)
Step 4: Determine the relationship between the speeds of Zebra and Buffalo.
The problem states that the speed of Buffalo is 20 km/h faster than Zebra. So we can write the equation:
Speed_Buffalo = Speed_Zebra + 20
Step 5: Use the relationship between distances traveled to solve for Speed_Buffalo.
Since both helicopters reach the same destination, the distances traveled by Zebra and Buffalo are equal. Therefore, we have the equation:
Distance_Zebra = Distance_Buffalo
Speed_Zebra × 3.5 = Speed_Buffalo × 1.5
Step 6: Solve the equation to find the speed of helicopter Buffalo.
Substituting Speed_Buffalo = Speed_Zebra + 20 into the equation from Step 5, we get:
Speed_Zebra × 3.5 = (Speed_Zebra + 20) × 1.5
Expanding the equation:
3.5 × Speed_Zebra = 1.5 × Speed_Zebra + 30
2 × Speed_Zebra = 30
Speed_Zebra = 15 km/h
Since Speed_Buffalo = Speed_Zebra + 20, we have:
Speed_Buffalo = 15 km/h + 20 km/h
Speed_Buffalo = 35 km/h
Therefore, the speed of helicopter Buffalo is 35 km/h.