SOLUTION: a cyclist rides her bike over a route that is 1/3 uphill, 1/3 level, and 1/3 downhill. If she covers the uphill part of the route at a rate of 16 km/h, and the level part at a rate

Question 933374: a cyclist rides her bike over a route that is 1/3 uphill, 1/3 level, and 1/3 downhill. If she covers the uphill part of the route at a rate of 16 km/h, and the level part at a rate of 24 km/h, what rate would she have to travel during the downhill part of the route in order to average 24 km/h for the entire route?
(ANS: 48km/h)
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
RT=D, T=D/R.

__________________rate__________time__________distance
UP________________16____________(___)__________d/3
LEV_______________24___________(____)__________d/3
DWN_______________(___)________(____)__________d/3
Total__________________________(____)__________d

__________________rate__________time__________distance
UP________________16____________(d/(3*16))__________d/3
LEV_______________24___________(d/(3*24))__________d/3
DWN_______________(r)________(d/(3r))__________d/3
Total__________________________(____)__________d

The total time would be ; which needs simplification before comfortably using this expression. The AVERAGE speed would be
;
LCD is 3*2*2*2*2, 3*2*2*2*3, 3*r,------;
---
Another way to continue is use reciprocals of both members.
-

Now multiply both members by LCD.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= 1/3 of the total route distance, in km, and
= the total route distance, in km.
Average time for the whole route = hours.
The time spent cycling uphill was hours, and
the time spent cycling on level was hours.
So, the time spent cycling downhill must have been
hours.
Then, the average speed in km/h cycling uphill for km in hours was
.

CHECKING:
Let's say that the total route is km.
That means km cycling downhill, at km/h, during hour,
km cycling on level ground, at km/h, during hours, and
km cycling uphill, at km/h, during hours,
for a total of km covered in hours,
at an average rate of km/h.

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