- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
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.