A pilot flew to Montreal and back . The average speed going was 320 mph , and the average speed returning was 480 mph. Find the distance to Montreal if the total flying time was 5 hours.
let the distance be d km
time on first trip = d/320
time on return trip = d/480
d/320 + d/480 = 5
the LCD is 960
3d/960 + 2d/960 = 5
5d/960 = 5
d/960 = 1
d = 960
(in Montreal they would use km and km/h, not miles and mph)
To find the distance to Montreal, we can use the formula:
Distance = Speed * Time
Let's denote the distance from the starting point to Montreal as D.
Given the average speed going was 320 mph and the average speed returning was 480 mph, we can calculate the time for each leg of the journey.
Using the formula Time = Distance / Speed, we can find the time it took to reach Montreal:
Time going = D / 320
Similarly, the time it took to return from Montreal:
Time returning = D / 480
We are given that the total flying time was 5 hours:
Total time = Time going + Time returning
Substituting the formulas for the times, we have:
5 = (D / 320) + (D / 480)
Now, we can solve this equation to find the value of D, which represents the distance to Montreal.
To do this, we can multiply both sides of the equation by the least common multiple (LCM) of 320 and 480, which is 960. This will help us eliminate the fractions:
5 * 960 = 960 * (D / 320) + 960 * (D / 480)
4800 = 3D + 2D
Combining like terms, we have:
4800 = 5D
To isolate D, we divide both sides of the equation by 5:
D = 4800 / 5
D = 960
Therefore, the distance to Montreal is 960 miles.