The respective ratio between the speeds of a car, a jeep and tractor is 3:5:2. The speed of the jeep is 250 percent of the speed of the tractor which covers 360 km in 12 hours. What is the average speed of car and jeep together ?
My Approach:
Let the speed of car be 3x
Let the speed of jeep be 5x
Let the speed of tractor be 2x
It's already given that tractor completes 360 km in 12 hours.
Applying the formula, speed * time = distance
speed of tractor = $\frac{distance}{time}$ = $\frac{360}{12}$ = 30km/hr
Therefore 2x = 30 => x=15
Speed of car = 3 * 15 = 45 km/hr
Speed of jeep = 5 * 15 = 75 km/hr
Average speed = $\frac{totaldistance}{totaltime}$
Let,
Distance covered by Car be = a
Distance covered by jeep be = b
Total distance = a+b
Time = $\frac{distance}{speed}$
Time(t1) covered by car =$\frac{a}{45}$
Time(t2) covered by jeep =$\frac{b}{75}$
Total time =$\frac{a}{45}$ + $\frac{b}{75}$ = $\frac{5a+3b}{225}$ (by taking lcm)
Now even if i apply these values to Average speed, I am not getting anywhere.
When i google this question, the solution contains this formula.
Average speed = $\frac{speed1+speed2}{2}$
Thus giving the answer as $\frac{45+75}{2}$=60km/hr.
If possible i want to know how this formula was derived [Average speed = $\frac{speed1+speed2}{2}$] ?
I don't understand. Please help .
[Update]
[Link] https://www.bankersadda.com/p/night-class-quantitative-aptitude-for_47.html ( Question 1)
Best Answer
The confusion you are running into is related to the following problem:
One reaction may be to say that the runner runs at an average speed of 9 meters per second: the average of 8 and 10. However, if we calculate the average speed of the runner fore the whole lap, we have to understand that the runner will be running at the slower speed for a longer period than that the runner runs at the greater speed. Hence, the average speed will be closer to 8 meters per second than to 10 meters per second. Indeed, the runner covers the first 200 meters in 20 seconds, and the second 200 meters in 25 seconds, for a total time of 45 seconds, resulting in an average speed of about 8.88 meters per second.
OK .... but what does this all mean as far as your question goes? I would say that the question is rather ambiguous in exactly these two ways. Maybe it is asking about the average of the speeds of the car and jeep ... which was the 'Google' answer. On the other hand, maybe we are asked to compute the average speed between the car and the jeep over some specific distance, compatible to how we computed the average speed of the runner over the whole 400 meter lap. ... And this is what you did .. and of course you got a different answer given that the car took a longer time covering that same distance than the jeep. So .. what were we being asked? I don't know ... I must say, I find this:
really quite unclear!