Question

While driving his car at a speed of 50 km/hr, Ramit covers a distance from home to his office in 1 hour 30 minutes. One day he was 15 minutes late from his home. In order to reach the office at time, what should be the speed of the car?
Also, find the total distance covered by Ramit daily.

Answer 1

Hint: Here we firstly know about the meaning of speed, distance, time, and their relations. The speed is defined by the ratio of distance and time. Now, we use the formula of \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\] for calculating the values speed of the car and the total distance covered by Ramit daily.

Complete step-by-step answer:
The given data are:
The speed of the car is 50 km/hr., the time taken by the Ramit is 1.5 hr., and the delayed or late time is 15 minutes.
Now, we use the formula of speed that is \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\]. Substitute the values of speed 50 km/hr. and time 1.5 hr. in the expression \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\].
\[ \Rightarrow 50 = \dfrac{{{\text{distance}}}}{{1.5}}\]
\[ \Rightarrow {\text{distance}} = 50 \times 1.5\]
\[ \Rightarrow {\text{distance}} = 75{\text{ km}}\]
Hence, the total distance covered by Ramit daily is 75 km.
Now, he is 15 minutes late, therefore he has to cover 75 km in 1 hr 15 minutes that is 1.25 hr.
Now, calculate the speed of the car by substituting the new time value 1.25 hr. in the expression \[ \Rightarrow {\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\].
\[ \Rightarrow {\text{speed}} = \dfrac{{75}}{{1.25}}\]
\[ \Rightarrow {\text{speed}} = 60{\text{ km/hr}}\]

Hence, the speed of the car is 60 km/hr.

Note: Make sure to use the same units or S.I units of all the given data. The S.I. units are the base units of the standard measurement units. So many students make errors when applying the units. First, convert all the values into S.I units after the necessary values have been determined. Every student should know the units of speed, distance, and time.