1. A travells a distance of 180 km in 5 hr. Find his speed in m/sec ?
Sol:
Speed = \(\frac{{180}}{5}\)
= 36 km/h
= 36 × \(\frac{5}{{18}}\)
= 10 m/sec Answer
2. A covers 32.5 km in 5 hours. Find the distance covered by him in 8 hours.
Sol:
3. A person goes from A to B at a speed of 30 km/h & returns from B to A at a speed of 10 km/h. What is the average speed for the whole journey ?
Sol:
Average Speed = \(\frac{{2 \times 10 \times 30}}{{10 + 30}}\) \(\left( {\frac{{2ab}}{{a + b}}} \right)\)
= 15 km/h Answer
4. A boy goes to a school at a speed of 3 km/h and returns at a speed of 2 km/h. If he takes 5 hr in all. find the distance between village & school.
Sol:
Method(1):
Average speed of journey = \(\frac{{2 \times 3 \times 2}}{{3 + 2}}\) = \(\frac{{13}}{5}\)
& total time = 5 hr
∴ 2d = \(\frac{{12}}{5}\) × 5
d = 6 km Answer
Method(2):
d = \(\frac{{{S_1} \times {S_2}}}{{{S_1} + {S_2}}} \times time\)
= \(\frac{{3 \times 2}}{{3 + 2}} \times 5\)
= 6 km Answer
5. A man goes from A to B at a speed of 20 km/h and returns at higher speed. If its average speed for the whole journey is 24 km/h, at what speed he returned ?
Sol:
24 = \(\frac{{2 \times 20 \times x}}{{20 + x}}\)
3 = \(\frac{{5 \times x}}{{20 + x}}\)
60 + 3x = 5x
x = 30 km/h Answer
6. In a journey of 240 km, a man covers a distance of 150 km at a speed of 75 km/h, the next 60 km distance at a speed of 100 km/h and the remaining distance at the speed of 75 km/h. Find the average speed for the whole journey.
Sol:
Avg speed = \(\frac{{total\;distance}}{{total\;time}}\)
= \(\frac{{240}}{{\frac{{150}}{{75}} + \frac{{60}}{{100}} + \frac{{30}}{{75}}}}\)
= \(\frac{{240}}{{2 + \frac{3}{5} + \frac{2}{5}}}\)
= \(\frac{{240 \times 5}}{{15}}\)
= 80 km/h Answer
7. A man went from Delhi to Lucknow via Bareilly by car. The distance from Delhi to Bareilly is \(\frac{3}{4}\) times the distance from Bareilly to Lucknow. the average speed from Delhi to Bareilly is \(\frac{3}{2}\) times the average speed from Bareilly to Lucknow. If the average speed for the entire journey was 56 km/h. What was the average speed from Bareilly to Lucknow ?
Sol:
Average speed of entire journey = 56 km/h
\(\frac{{7x}}{{\frac{{3x}}{{2y}} + \frac{{4x}}{{2y}}}}\) = 56
\(\frac{{7y}}{3}\) = 56
y = 24 km/h
∴ avg speed from Bareilly to Lucknow = 2y
= 48 km/h Answer
8. A car during its journey travells 30 minutes at a speed of 20 km/h, another 12 minutes at a speed of 50 km/h and 1 hour at a speed of 48 km/h. Find the average speed of the car ?
Sol:
Average speed = \(\frac{{20 \times \frac{{30}}{{60}} + 50 \times \frac{{12}}{{60}} + 48 \times 1}}{{\frac{{30}}{{60}} + \frac{{12}}{{60}} + 1}}\)
= \(\frac{{10 + 10 + 48}}{{\frac{{17}}{{10}}}}\)
= \(\frac{{68 \times 10}}{{17}}\)
= 40 km/h Answer
9. A starts his journey from Delhi to Jaipur and simultaneously B starts from Jaipur to Delhi. After crossing each other they finish their remaining journey in \(9\frac{4}{5}\) hours & 5 hours respectively. What is A’s speed if B’s speed is 35 km/h ?
Sol:
\(\frac{A}{{35}} = \sqrt {\frac{5}{{9\frac{4}{5}}}} = \sqrt {\frac{{25}}{{49}}} = \frac{5}{7}\)
A = 28 km/h Answer
10. Two persons covers the same distance at a speed of 40 km/h & 30 km/h respectively. Find the distance travelled if one person takes 15 min more than the other.
Sol:
Method(1):
distance = \(\frac{{{S_1} \times {S_2}}}{{{S_1} – {S_2}}}\) × (diff. in time)
= \(\frac{{40 \times 30}}{{40 – 30}} \times \frac{{15}}{{60}}\)
d = 30 km Answer
Method(2):
Since distance is constant