Speed Time And Distance - Study Mode

[#171] Train X leaves New York at 1 am and travels east at a constant speed of x mph. If train Z leaves New York at 2 am and travels east, at what constant rate of speed will train Z have to travel in order to catch train X at exactly 5.30 am ?
Correct Answer

(D) $$frac{9}{7}x$$

Explanation

Solution: Let the speed of train Z be z mph Distance travelled by train X in 1 hr = x miles Relative speed of train Z w.r.t. train X = (z - x) mph To catch train X at 5.30 am, train Z will have to cover x miles at relative speed in 3 hr 30 min, i.e., $$frac{7}{2}$$ hrs $$eqalign{
& herefore left( {z - x}
ight) imes frac{7}{2} = x cr
& Rightarrow frac{7}{2}z = frac{9}{2}x cr
& Rightarrow z = left( {frac{9}{2} imes frac{2}{7}}
ight)x cr
& Rightarrow z = frac{9}{7}x cr} $$

[#172] A car goes 20 metres in a second. Find its speed in km/hr ?
Correct Answer

(B) 72 km/hr

Explanation

Solution: 1 m/sec = $$frac{18}{5}$$ km/hr Car cover 20 metres in a second ∴ 20 m/sec = $$frac{20 ×18}{5}$$ xa0= 72 km/hr

[#173] A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speed is :
Correct Answer

(A) 3 : 4
(G) 3 : 4

Explanation

Solution: Ratio of speeds : $$eqalign{
& = left( {frac{{550}}{{60}} imes frac{{18}}{5}}
ight):left( {frac{{33}}{{45}} imes 60}
ight) cr
& = 33:44 cr
& = 3:4 cr} $$

[#174] A person wishes to reach his destination 90 km away 3 hours but for the first half of the journey his speed was 20 km/hr. His average speed for the rest of the journey should be :
Correct Answer

(C) 1 km/min

Explanation

Solution: Time taken to travel 45 km : $$eqalign{
& = left( {frac{{45}}{{20}}}
ight){ ext{ hrs}} cr
& = frac{9}{4}{ ext{ hrs}} cr
& = 2frac{1}{4}{ ext{ hrs}} cr
& = 2{ ext{ hrs }}15min cr} $$ Remaining time = (3 hrs - 2 hrs 15 min) = 45 min Hence, required speed : $$eqalign{
& = left( {frac{{45}}{{45}}}
ight){ ext{ km/min}} cr
& = 1{ ext{ km/min}} cr} $$

[#175] The distance between two places R and S is 42 km. Anita starts from R with a uniform speed of 4 km/hr towards S and at the same time Romita starts from S towards R also with some uniform speed. They meet each other after 6 hours. The speed of Romita is :
Correct Answer

(C) 3 km/hr

Explanation

Solution: Let speed of Romita be x km According to the question, (4 + x) = $$frac{42}{6}$$ $$left( {{ ext{S = }}frac{{ ext{D}}}{{ ext{T}}}}
ight)$$ 4 + x = 7 x = 3 km/hr