scthakur wrote:

Question has lots of wordings to make it appear complex. However, what essentially it means that the fly would travel at a constant speed of 10kmph for the time taken by the hiker(s) to travel 15 km.

You cannot assume that the fly flies back to hiker K from hiker R at 10km/hr. If you assume that, then the fly meets hiker K

before hiker K and hiker R meet.

The fly meets hiker R after 2hours:

-The fly has traveled 20km and hiker R has traveled 10km toward K.

-Hiker K has also traveled 10 km toward R.

-At this point hiker K and hiker R are 10km apart.

Now the fly goes back to hiker K, if we assume that the fly is flying at 10km/hr toward hiker K, we need to consider that hiker K is traveling at 5km/hr toward the fly. Therefore we need to add their rates to find out how long it takes for them to meet.

distance between / combined rates = time it takes

10 km / (5 km/hr + 10 km/hr) = 2/3 hr.

now add the flight times for the fly, 2hr + 2/3hr = 8/3 hr.

So the fly has flown for 10km/hr * (8/3 hr) = 80/3 km = 26.67 km

Another thing problematic with this question:

The stimulus never states that the fly flew back at 10km/hr, it simply states that it flew back to hiker K at the same time that they met.

If we don't assume that the fly flies back at 10km/hr:

After the fly has met hiker R, the two hikers are 10km apart. If it flies back and lands on hiker K's shoulder at the same time that hiker K and hiker R meet, it has to travel at a slower speed than 10km/hr (it has to travel at 5km/hr -- the same speed as the hikers). Thus it travels another 5km.

Therefore it has travelled 20km (until it met hiker R) then traveled back 5km (at a slower speed) for a total of 25km

So I think the OA is incorrect.This is a badly worded question in my opinion. It also forces you to make certain assumptions:

1. the fly is flying constantly at the same speed. (even using this assumption it doesn't work out)

2. the fly only flies in a straight line. (I've never seen a fly fly in a straight line -- the fly could actually have covered alot more distance if it didn't fly in a straight line)

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