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Question #22008
on a 40km bike ride a cyclist rides the first 20km at 20km/h. what is the speed require for the final 20km if the average speed for the trip is to be 10km/h?
1
2013-01-23T08:35:23-0500
Let&#039;s denote the average speed for the trip by V (V = 10km/h), the speed for the first 20km by V1 (V1 = 20km/h) and the speed for the last 20km by V2 (V2 is unknown), the first and the second parts of a distance by S1 and S2 (s1 = S2 = 20[km]), and the time for the first and the second parts of a distance by T1 and T2 respectfully. Then

V&middot;(T1 + T2) = V1&middot;T1 + V2&middot;T2 (1)

A cyclist spent

T1 = 20[km]/20[km/h] = 1[h]

riding the first 20km at 20km/h. Also, he spent

T1 = S2/V2

riding the second 20km. So, we can rewrite (1) as

V&middot;(T1 + S2/V2) = V1&middot;T1 + V2&middot;S2/V2,

or

V&middot;T1 + V&middot;S2/V2 = V1&middot;T1 + S2 ==&gt;

V2 = V&middot;S2 / ( V1&middot;T1 + S2 - V&middot;T1 ) =

= 10[km/h]&middot;20[km] / (20[km/h]&middot;1[h] + 20[km] - 10[km/h]&middot;1[h] ) =

= 10[km/h]&middot;20[km] / 30[km] = 20/3 [km/h].

Therefore, the speed required for the final 20km if the average speed for the trip to be 10km/h is 20/3 [km/h].

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