Question

A bus takes 10 hours to reach a destination by travelling at a speed of 65 km/h. If the same journey is to
be completed in 13 hours, then what will be the speed of the bus?​

Answer 1

Given :

• Time taken by the bus to reach a destination by travelling with a speed of 65 km/h is 10 hours
• Time Taken by the bus to complete the same journey with some particular speed is 13 hours

To Find :

• Speed of the bus when the bus takes 13 hours to complete the same journey

Solution :

$\Large\underline{\bf{\green{Case-I:}}}$

Speed of the bus = 65 km/hr

Time taken = 10 hours

Now , The Distance travelled by the bus is given by ,

$\\ \star \: {\boxed{\sf{\purple{distance = speed \times time}}}}$

Substituting the values ,

$\\ : \implies \sf \: d = 65 \: km {hr}^{ - 1} \times 10 \: h$

$\\ : \implies \sf \: d = 65 \: km \times 10$

$\\ : \implies{\boxed{\red{\sf{ \: d = 650 \: km}}}} \:$

The distance travelled by the bus is 650 km.

$\Large\underline{\bf{\green{Case-II:}}}$

Time taken by the bus to complete the same journey = 13 hours

Distance = 650 km (Since it is the same journey)

Now , Applying the relation between Distance , Speed and time . We get ;

$\\ : \implies \sf \: 650 \: km = s \times 13 \: h$

$\\ : \implies \sf \: s = \frac{650 \: km}{13 \: h}$

$\\ : \implies{\boxed{\pink{\sf {\: s = 50 \: km {hr}^{ - 1} }}}} \: \bigstar$

Hence , The speed of the bus when it completes the same journey within 13 hours is 50 km/hr