Speed Time And Distance - Study Mode

[#151] An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in $$1frac{2}{3}$$ hours, it must travel at a speed of :
Correct Answer

(D) 720 kmph

Explanation

Solution: $$eqalign{
& ext{Distance}=left(240 imes5
ight) ext{ km} cr
& ,,,,,,,,,,,,,,,,,,,,,, ext{ = 1200 km} cr
& herefore ext{ Required Speed:} cr
& = frac{ ext{Distance}}{ ext{Time}} cr
& = frac{1200}{frac{5}{3}} cr
& = left( {1200 imes frac{3}{5}}
ight){ ext{ km/hr}} cr
& = 720{ ext{ kmph}} cr} $$

[#152] A man on tour travels 160 km by car at 64 km/hr and another 160 km by bus at 80 km/hr. The average speed for the whole journey is :
Correct Answer

(C) 71.11 km/hr

Explanation

Solution: Total time taken : $$eqalign{
& = left( {frac{{160}}{{64}} + frac{{160}}{{80}}}
ight){ ext{ hrs}} cr
& = frac{9}{2}{ ext{ hrs}} cr} $$ ∴ Average speed : $$eqalign{
& = left( {320 imes frac{2}{9}}
ight){ ext{ km/hr}} cr
& = 71.11{ ext{ km/hr}} cr} $$

[#153] A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is :
Correct Answer

(C) 120 kmph

Explanation

Solution: Let speed of the car be x kmph Then, speed of the train : $$ = frac{{150}}{{100}}x = left( {frac{3}{2}x}
ight){ ext{ kmph}}$$ $$eqalign{
& herefore frac{{75}}{x} - frac{{75}}{{frac{3}{2}x}} = frac{{125}}{{10 imes 60}} cr
& Leftrightarrow frac{{75}}{x} - frac{{50}}{x} = frac{5}{{24}} cr
& Leftrightarrow x = left( {frac{{25 imes 24}}{5}}
ight) cr
& Leftrightarrow x = 120{ ext{ kmph}} cr} $$

[#154] A and B start from the same point and in the same direction at 7 am to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other if they continue to walk till 12.30 pm ?
Correct Answer

(B) Once

Explanation

Solution: Perimeter of the field = 2(400 + 300) m = 1400 m = 1.4 km Since A and B move in the same direction, so they will first meet each other when there is a difference of one round i.e., 1.4 km between the two. Relative speed of A and B = (3 - 2.5) km = 0.5 km/hr Time take to cover 1.4 km at this speed : $$eqalign{
& = left( {frac{{1.4}}{{0.5}}}
ight){ ext{ hr}} cr
& = 2frac{4}{5}{ ext{ hr}} cr
& = 2{ ext{ hr 48 min}} cr} $$ So, they shall first cross each other at 9.48 am And again 2 hr 48 min after 9.48 am i,e., 12.36 pm Thus, till 12.30 pm they will cross each other once.

[#155] The driver of an ambulance sees a school bus 40 m ahead of him after 20 seconds, the school bus is 60 meter behind. If the speed of the ambulance is 30 km/h, what is the speed of the school bus?
Correct Answer

(B) 12 kmph

Explanation

Solution: Relative Speed,
$$eqalign{
& = frac{{{ ext{Total }},{ ext{distance}}}}{{{ ext{Total time}}}} cr
& = frac{{60 + 40}}{{20}} cr
& = 5,,{ ext{m/s}} cr
& = frac{{5 imes 18}}{5} cr
& = 18,,{ ext{kmph}} cr} $$ Relative Speed = (speed of ambulance - speed of school bus) Speed of school bus = speed of ambulance - relative speed. = 30 - 18 = 12 kmph.