1) A cyclist travels uphill from A to B, a distance of 24km at an average speed of 12km/h. On the return journey downhill, his average speed is 36km/h. What is his average speed in kilometres per hour for the whole journey?
2) In a group of 40 students, 20 play tennis, 19 play volleyball and 6 play both tennis and volleyball. What is the number of students who play neither tennis nor volleyball?
Thanks in advance.
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Answers & Comments
Verified answer
1)
Let D be the distance traveled uphill. Then, since the distance traveled downhill is also D (since it's the same distance), the total distance traveled is 2D.
Since traveling D km at 24km/h takes D/24 hours and traveling D km at 36 km/h takes D/36 hours, we have that the average speed is:
d = rt
==> r = d/t = 2D/(D/24 + D/36) = 2/(1/24 + 1/36) = 28.8 km/h.
2)
If we total the number given that play tennis and volleyball, we get 20 + 19 = 39. However, since this over-counts the actual amount by 6 as 6 players are counted twice (because they are on both teams), the actual number of people playing tennis or volleyball is 39 - 6 = 33 and so 40 - 33 = 7 people are playing neither.
I hope this helps!
Let T denote set of students who play tennis
No.of students who play tennis = n(T) = 20
Let V denote set of students who play volleyball
No. of students who play volleyball = n(V) = 19
No. of students who play both tennis and volleyball = n(T∩V) = 6
No. of students who play tennis or volleyball = n(TUV)
n(TUV) = n(T) + n(V) - n(T∩V)
n(TUV) = 20 + 19 - 6
n(TUV) = 33
No. of students who play tennis or volleyball = n(TUV) = 33
No. of students who play neither tennis nor volleyball = 40 -33 = 7