Speed Time And Distance - Study Mode

[#256] A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance?
Correct Answer

(A) 5 hours 45 minutes

Explanation

Solution: $$eqalign{
& frac{{40}}{A} - frac{{40}}{B} = 2frac{1}{2} = frac{5}{2}{ ext{ }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}left( { ext{i}}
ight) cr
& frac{{40}}{B} - frac{{40}}{{2A}} = 1{ ext{ }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}{ ext{. }}left( {{ ext{ii}}}
ight) cr
& { ext{Equation }}left( { ext{i}}
ight) + { ext{Equation }}left( {{ ext{ii}}}
ight) cr
& frac{{40}}{A} - frac{{40}}{{2A}} = frac{5}{2} + 1 cr
& frac{{40}}{A} - frac{{40}}{{2A}} = frac{7}{2} cr
& frac{{40}}{{2A}} = frac{7}{2} cr
& A = frac{{40}}{7} cr
& { ext{Put the value of A in equation }}left( { ext{i}}
ight) cr
& 7 - frac{{40}}{B} = frac{5}{2} cr
& 7 - frac{5}{2} = frac{{40}}{B} cr
& frac{9}{2} = frac{{40}}{B} cr
& B = frac{{80}}{9} cr
& { ext{Now, required answer}} cr
& = frac{{frac{{40}}{{frac{{40}}{7}}} + frac{{40}}{{frac{{80}}{9}}}}}{2} cr
& = frac{{7 + frac{9}{2}}}{2} cr
& = frac{{23}}{4} cr
& = 5frac{3}{4} cr
& = 5{ ext{ hours }}45{ ext{ minutes}} cr} $$

[#257] Two cars start from the same place at the same time at right angles to each other. Their speeds are 54 km/hr and 72 km/hr, respectively. After 20 seconds the distance between them will be:
Correct Answer

(D) 500 m

Explanation

Solution: 54 km/h = 54 × $$frac{5}{{18}}$$ = 15 m/s 72 km/h = 72 × $$frac{5}{{18}}$$ = 20 m/s The distance of BC = 15 × 20 = 300 m The distance of AB = 20 × 20 = 400 $${ ext{AC}} = sqrt {{{400}^2} + {{300}^2}} = 500$$

[#258] A person covers 40% of the distance from A to B at 8 km/h, 40% of the remaining distance at 9 km/h and the rest at 12 km/h. His average speed (in km/h) for the journey is:
Correct Answer

(C) $$9frac{3}{8}$$
(G) $$9frac{3}{8}$$

Explanation

Solution: $$eqalign{
& { ext{Let total distance}} = 100 cr
& { ext{Average speed}} = frac{{{ ext{Total distance}}}}{{{ ext{Total time}}}} cr
& = frac{{100}}{{frac{{40}}{8} + frac{{24}}{9} + frac{{36}}{{12}}}} cr
& = frac{{100}}{{5 + frac{8}{3} + 3}} cr
& = frac{{100 imes 3}}{{32}} cr
& = frac{{75}}{8} cr
& = 9frac{3}{8} cr} $$

[#259] Richa travels from A to B at the speed of 15 km/h, from B to C at 20 km/h, and from C to D at 30 km/h. If AB = BC = CD, then find the Richa's average speed.
Correct Answer

(D) 20 km/h
(H) 20 km/h

Explanation

Solution: $$eqalign{
& { ext{Distance}} = { ext{ LCM of }}15,,20,,30 = 60{ ext{ km}} cr
& { ext{Average speed}} = frac{{{ ext{Total distance}}}}{{{ ext{Total time}}}} cr
& = frac{{3 imes 60}}{{4 + 3 + 2}} cr
& = frac{{180}}{9} cr
& = x08oxed{20{ ext{ km/h}}} cr} $$

[#260] A man travelled a distance of 1200 km in 16 hours, He travelled partly by car at a speed of 40 km/h, and partly by train at a speed of 80 km/h. What is the distance traveled by car?
Correct Answer

(D) 80 km

Explanation

Solution: 8 unit ⟶ 16 hour 1 unit ⟶ 2 hour Car = 2 hour = 2 × 40 = 80 km