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
- A car is moving on a horizontal surface in a straight line with a constant velocity of 3 m/s. A ball is thrown vertically upwards at time $t = 0$ from the top of the moving car with a velocity of 20 m/s. The acceleration due to gravity is 10 m/s$^2$.
At what value(s) of time $t$ in second(s), the ball is at a height of 15 m from the top of the moving car? - Velocity of an object fired directly in upward direction is given by $V = 80 – 32 \ t$, where $t$ (time) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?
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?- An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?
Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ___________.
