A plane flew from Red Deer to Winnipeg, a flying distance of 1260 km. On the return journey, due to strong head wind, the plan travelled 1200 km in the same time it took to complete the outward journey. On the outward journey, the plane was able to maintain an average speed of 42km/hr greater than on the return journey. Calculate the average speed of the plane from Winnipeg to red deer.
Given: when the plane is going from red deer to Winnipeg distance travelled {eq}= 1260{/eq} km.
On returning distance travelled {eq}= 1200{/eq} km
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time = distance/speed, so
1260/(s+42) = 1200/s
To find the average speed of the plane from Winnipeg to Red Deer, we can start by calculating the time it took for each leg of the journey.
Let's assume the average speed of the plane on the return journey (from Winnipeg to Red Deer) is x km/hr.
On the outward journey (from Red Deer to Winnipeg), the plane's average speed is 42 km/hr greater than on the return journey, so it would be (x + 42) km/hr.
Distance = Speed × Time, so we can calculate the time it took for each leg of the journey:
Outward journey: Time = Distance / Speed = 1260 km / (x + 42) km/hr
Return journey: Time = Distance / Speed = 1200 km / x km/hr
Since the return journey took the same time as the outward journey, we can set up the equation:
1260 / (x + 42) = 1200 / x
Now, we can cross-multiply and solve for x:
1260x = 1200(x + 42)
1260x = 1200x + 50400
1260x - 1200x = 50400
60x = 50400
x = 840
Therefore, the average speed of the plane from Winnipeg to Red Deer is 840 km/hr.