A boy was riding his bicycle. He rode at a speed of 9 km/h for the first 10 minutes. At what speed he should ride for the next 20 minutes so that his average speed for 30 minutes comes out to be 12 km/h?

Given,

Speed (S₁) = 9km/h

Time (t₁) = 10m = $\frac{10}{60}h$ = $\frac{1}{6}h$        [converted minutes into hours]

Speed (S₂) = ?                               [to find]

Time (t₂) = 20m = $\frac{20}{60}h$  $\frac{1}{3}h$          [converted minutes into hours]

Total time taken (t) = (t₁+ t₂) = (10m + 20m) = 30m = $\frac{30}{60}h$=$\frac{1}{2}h$ 

Average Speed (S) = 12km/h

Here, given multiple speeds for different amounts of time, so total distance can be given as-

$D={S}_{1}\times {t}_{1}+{S}_{2}\times {t}_{2}$                 $[\because D=S\times t]$

We know that Average speed is the ratio of total distance travelled and the total time taken.

It is given as-

$Average\ Speed\ (S)=\frac{Total\ distance\ \ travelled\ (d)}{Total\ time\ \ taken\  (t)}$

$S=\frac{{S}_{1}\times {t}_{1}+{S}_{2}\times {t}_{2}}{{t}_{1}+{t}_{2}}$

Now, substituting the value-

$12=\frac{9\times \frac{1}{6}+{S}_{2}\times \frac{1}{3}}{\frac{1}{2}}$

$12=\frac{\frac{9+2{S}_{2}}{6}}{\frac{1}{2}}$

$12=\frac{9+2{S}_{2}}{6}\times \frac{2}{1}$

$12=\frac{9+2{S}_{2}}{3}$

$12\times 3=9+2{S}_{2}$

$36-9=2{S}_{2}$

${S}_{2}=\frac{27}{2}$

${S}_{2}=13.5km/h$

Thus, $13.5km/h$ is the speed at which the boy should ride his bicycle for the next 20 minutes so that his average speed for 30 minutes comes out to be 12 km/h.

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Updated on: 10-Oct-2022

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