Speed Time And Distance - Study Mode

[#236] A car can finish a certain journey in 10 hours at a speed of 42 kmph. In order to cover the same distance in in 7 hours, the speed of the car (km/h) must be increased by :
Correct Answer

(C) 18 km/hr

Explanation

Solution: Total distance : = 42 × 10 = 420 km New given time = 7 hr and Required new speed : = $$frac{420}{7}$$ km/hr = 60 km/hr ∴ Required increase in speed : = (60 - 42) km/hr = 18 km/hr

[#237] Two cars start at the same time from in point and move alone two roads, at right angle to each other. The speeds are 36 km/hr and 48 km/hr respectively. After 15 sec distance between them will be :
Correct Answer

(D) 250 m

Explanation

Solution: Distance travelled by the 1st car in 15 seconds $$eqalign{
& { ext{OA}} = left( {36 imes frac{5}{{18}}}
ight) imes 15,{ ext{m}} cr
& ,,,,,,,,,,, = 150,{ ext{m}} cr} $$ Distance travelled by the 2nd car in 15 seconds $$eqalign{
& { ext{OB}} = left( {48 imes frac{5}{{18}}}
ight) imes 15,{ ext{m}} cr
& ,,,,,,,,,, = 200,{ ext{m}} cr} $$ ∴ Distance between them after 15 seconds $$eqalign{
& { ext{AB}} = sqrt {{ ext{O}}{{ ext{A}}^2} + { ext{O}}{{ ext{B}}^2}} cr
& ,,,,,,,,,, = sqrt {{{150}^2} + {{200}^2}} cr
& ,,,,,,,,,, = sqrt {22500 + 40000} cr
& ,,,,,,,,,, = sqrt {62500} cr
& ,,,,,,,,,, = 250,{ ext{m}} cr} $$

[#238] A train is moving at a speed of 80 km/hr and covers a certain distance in 4.5 hours. The speed of the train to cover the same distance in 4 hours is :
Correct Answer

(D) 90 km/hr

Explanation

Solution: In the first situation, ⇒ Total distance covered by train : = 80 × $$4frac{1}{2}$$ = 360 kms ⇒ Therefore, The speed of the train to cover the same distance 360 km in 4 hours is : $$eqalign{
& = frac{{360}}{4}left{ {{ ext{Speed }} = frac{{{ ext{Distance }}}}{{{ ext{Time}}}}}
ight} cr
& = 90{ ext{ km/h}} cr} $$

[#239] A constable is 114 metre behind a thief. The constable runs 21 metres per minute and the thief runs 15 metres in a minute. In what time will the constable catch the thief ?
Correct Answer

(A) 19 min

Explanation

Solution: $$eqalign{
& {{ ext{V}}_{{ ext{rel}}{ ext{.}}}} = left( {21 - 15}
ight){ ext{ m/min}} cr
& ,,,,,,,,,,, = { ext{ 6 m/min}} cr} $$ Time taken to catch the thief : = $$frac{114}{6}$$ min = 19 min

[#240] A boy rides his bicycle 10 km at an average speed of 12 km/hr and travells 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately :
Correct Answer

(B) 10.8 km/hr

Explanation

Solution: $$eqalign{
& { ext{Average speed }} = frac{{{ ext{Total distance }}}}{{{ ext{Total time}}}} cr
& { ext{Average speed }} = frac{{{ ext{10 + 12 }}}}{{frac{{10}}{{12}} + frac{{12}}{{10}}}} cr
& { ext{Average speed }} = 10.8{ ext{ km/hr}} cr} $$