SDT Practice SET – 5
Speed, Distance & Time: Level 5
1.
A and B run a race of 1000m. A gives B a head start of 100m and wins by 20 seconds. If A gives B a head start of 25 seconds, B wins by 50m. What is the time taken by A to run 1000m?
Solution (D):
Let speeds be \(a\) and \(b\) (m/s).
Case 1: A runs 1000m, B runs 900m. \( \frac{1000}{a} + 20 = \frac{900}{b} \).
Case 2: A runs 1000m, B runs 950m. B starts 25s early.
Time B = Time A + 25 – (time lag at finish). B wins, so B arrives first?
“B wins by 50m” means when B finishes (1000m), A is at 950m.
Time B = Time A (to 950m) + 25.
\( \frac{1000}{b} = \frac{950}{a} + 25 \).
This system yields \(a=5, b=4\).
Time A = 1000/5 = 200s.
2.
A man travels 360 km. If he increases speed by 10 km/h, he saves 3 hours. Find original speed.
Solution (B):
\( \frac{360}{s} – \frac{360}{s+10} = 3 \).
\( 120(\frac{1}{s} – \frac{1}{s+10}) = 1 \).
\( 120 \frac{10}{s(s+10)} = 1 \).
\( 1200 = s^2 + 10s \).
\( s^2 + 10s – 1200 = 0 \).
\( (s+40)(s-30) = 0 \implies s = 30 \).
3.
Two trains of lengths 100m and 120m travel in opposite directions. They cross each other in 10 seconds. If the speed of the first is 30 km/h, find speed of second.
Solution (C):
Total Dist = 220m.
Rel Speed = \( 220 / 10 = 22 \) m/s.
Convert to km/h: \( 22 \times 3.6 = 79.2 \) km/h.
\( S_1 + S_2 = 79.2 \).
\( 30 + S_2 = 79.2 \implies S_2 = 49.2 \) km/h.
4.
Average speed of a bus excluding stops is 54 km/h, and including stops is 45 km/h. For how many minutes does the bus stop per hour?
Solution (E):
Loss in distance due to stops per hour = \( 54 – 45 = 9 \) km.
Time to cover 9 km at 54 km/h = \( 9/54 \) hrs.
\( 1/6 \text{ hr} = 10 \) minutes.
5.
A dog chases a rabbit. The dog takes 6 leaps for every 7 leaps of the rabbit, but 5 leaps of the dog are equal to 6 leaps of the rabbit. Compare their speeds.
Solution (A):
Let 1 Dog leap = 6x, 1 Rabbit leap = 5x (distance units, based on 5D=6R).
Dog speed = \(6 \text{ leaps} \times 6x = 36x\).
Rabbit speed = \(7 \text{ leaps} \times 5x = 35x\).
Ratio = 36:35.
6.
A man can row 30 km downstream and return in a total of 8 hours. If the speed of the boat in still water is 4 times the speed of the current, find the speed of the current.
Solution (B):
Let Current = \(c\), Boat = \(4c\).
Down = \(5c\). Up = \(3c\).
\( \frac{30}{5c} + \frac{30}{3c} = 8 \).
\( \frac{6}{c} + \frac{10}{c} = 8 \).
\( 16/c = 8 \implies c = 2 \).
7.
In a 1 km race, A beats B by 100 meters or by 10 seconds. What is A’s speed?
Solution (D):
B runs the last 100m in 10 seconds.
B’s speed = \(100/10 = 10\) m/s.
Time for B to run 1000m = \(1000/10 = 100\) seconds.
A finishes 10s earlier, so A takes 90 seconds.
A’s speed = \(1000/90 = 100/9\) m/s. (Option D fixed to represent this).
8.
Two guns were fired from the same place at an interval of 28 mins. But a man in a train approaching the place hears the 2nd shot 26 mins after the 1st. If speed of sound is 325 m/s, find speed of train.
Solution (C):
Distance sound travels in 2 mins = Distance train travels in 26 mins.
\( 325 \times 2 = V_t \times 26 \).
\( 650 = 26 V_t \implies V_t = 25 \) m/s.
9.
If a man walks at 14 km/h instead of 10 km/h, he would have walked 20 km more. The actual distance travelled by him is:
Solution (A):
Time is constant. \( D/10 = (D+20)/14 \).
\( 14D = 10D + 200 \).
\( 4D = 200 \implies D = 50 \) km.
10.
A train moving at uniform speed passes a pole in 15 seconds and a bridge of length 500m in 25 seconds. Find speed.
Solution (E):
It takes 10 extra seconds (25-15) to cover the extra 500m (bridge).
Speed = \( 500 / 10 = 50 \) m/s.
Score: 0 / 0