Problem Setup: Budhan's Journey
We need to find Budhan's walking speed. Let '$S_w$' represent the walking speed in km/h and '$S_c$' represent the cycling speed in km/h.
The total time for both days is 2 hours.
Day 1 Calculation
Budhan cycles for $\frac{1}{4}$ of the time and walks for the rest.
- Time cycling = $\frac{1}{4} \times 2$ hours = 0.5 hours.
- Time walking = $2 - 0.5$ hours = 1.5 hours.
- Total distance = 19 km.
- Using Distance = Speed $\times$ Time, we get the equation: $ S_c \times 0.5 + S_w \times 1.5 = 19 \quad \cdots (1) $
Day 2 Calculation
Budhan cycles for $\frac{1}{2}$ of the time and walks for the rest.
- Time cycling = $\frac{1}{2} \times 2$ hours = 1 hour.
- Time walking = $2 - 1$ hour = 1 hour.
- Total distance = 26 km.
- The equation for Day 2 is: $ S_c \times 1 + S_w \times 1 = 26 \quad \cdots (2) $
Solving for Walking Speed ($S_w$)
We have a system of two linear equations:
- $0.5 S_c + 1.5 S_w = 19$
- $S_c + S_w = 26$
From Equation (2), we can express the cycling speed '$S_c$' in terms of walking speed '$S_w$': $ S_c = 26 - S_w $
Now, substitute this expression for '$S_c$' into Equation (1): $ 0.5 (26 - S_w) + 1.5 S_w = 19 $
Distribute the 0.5:
$ 13 - 0.5 S_w + 1.5 S_w = 19 $
Combine the '$S_w$' terms:
$ 13 + 1.0 S_w = 19 $
Isolate the '$S_w$' term:
$ S_w = 19 - 13 $
$ S_w = 6 $
The walking speed is 6 km/h.
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.
