Determine Car P's Distance
Car P starts at 10 AM and travels continuously until 11:30 AM. The total time duration is 1 hour and 30 minutes, which is $1.5$ hours.
Speed of Car P = $25$ km/h. Distance covered by Car P = Speed $\times$ Time Distance$_P = 25 \text{ km/h} \times 1.5 \text{ h} = 37.5 \text{ km}$.
Determine Car Q's Required Moving Time
The problem states that at 11:30 AM, both cars are the same distance from the starting point X. Therefore, the distance covered by Car Q must also be $37.5$ km.
Speed of Car Q = $30$ km/h. Let $T_{move\_Q}$ be the total time Car Q was moving. Distance$_Q$ = Speed$_Q \times T_{move\_Q}$ $37.5 \text{ km} = 30 \text{ km/h} \times T_{move\_Q}$
Solving for $T_{move\_Q}$: $T_{move\_Q} = \frac{37.5 \text{ km}}{30 \text{ km/h}} = 1.25 \text{ hours}$.
Calculate Car Q's Stopping Time
The total time elapsed from 10 AM to 11:30 AM is $1.5$ hours. This total time is the sum of the time Car Q was moving ($T_{move\_Q}$) and the time it was stopped ($T_{stop\_Q}$). Total Time = $T_{move\_Q} + T_{stop\_Q}$ $1.5 \text{ h} = 1.25 \text{ h} + T_{stop\_Q}$
Solving for $T_{stop\_Q}$: $T_{stop\_Q} = 1.5 \text{ h} - 1.25 \text{ h} = 0.25 \text{ hours}$.
Convert Stopping Time to Minutes
To express the stopping time in minutes: Stopping Time (in minutes) = $0.25 \text{ hours} \times 60 \text{ minutes/hour}$ Stopping Time = $15$ minutes.
Verification: Car Q travels for 1 hour (10 AM to 11 AM, covers 30 km). Then it stops for 15 minutes (11 AM to 11:15 AM). Then it travels again for the remaining 0.25 hours (11:15 AM to 11:30 AM, covers $30 \times 0.25 = 7.5$ km). Total distance for Q = $30 + 7.5 = 37.5$ km. This matches Car P's distance.
Important Questions from Speed Distance and Time
- Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of 25 km/h and car Q travels East with a speed of 30 km/h. Car P travels continuously but car Q stops for some time after travelling for one hour. If both the cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?
In a 500 m race, P and Q have speeds in the ratio of 3: 4. Q starts the race when P has already covered 140 m.
What is the distance between P and Q (in m) when P wins the race?A vehicle is moving at a speed of 12 m/s on a level road. It applies emergency brakes and starts to skid without rolling in a straight path. The deceleration of the vehicle is constant after braking and it comes to rest at a distance of 15 m. Assuming, $g = 10$ m/s$^2$, the coefficient of kinetic friction between the tyres and road is _________ [round off to 2 decimal places]
- The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?
Two trains started at 7AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km apart is _______________ AM.
