# Time distance speed questions

Time, Speed, and Distance questions have high weightage in competitive tests and require thorough preparation. Although the concepts remain the same, the questions on examinations may vary. Many of them are challenging and confusing. To get better marks on competitive exams, practice the time, speed, and distance questions and their solutions. Find the questions for free now!

1. A train traveling at 60 kmph crosses another train traveling in the same direction at 24 kmph in 30 seconds. What is the combined length of both the trains?

As both the trains are moving in the same direction,

the relative speed of the faster train is 60 – 24 = 36 kmph.

The relative speed in m/sec = 36 x 5/18 = 10 m/sec.

Time taken = 30 sec.

Therefore, distance traveled = 10 × 30 = 300 m = Combined length of two trains.

1. Ananya and Gopika leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Ananya takes 4 hours to reach her destination, while Gopika takes 9 hours to reach his destination. If the speed of Ananya is 48 km/hr, what is the speed of Gopika?

Ananya and Gopika travel for the same amount of time till the time they meet between x and y.

So, the distance covered by them will be the same as the ratio of their speeds. Let the time that they have taken to meet each other be xx hours from the time they have started.

Therefore, the cover the entire distance, Ananya would take x+4 hours and Gopika will take x+9 hours.

Ratio of time taken Ananya : Gopika :: x+4:x+9

⇒ Ratio of speeds of Ananya : Gopika :: x+9:x+4or $1:\frac{x+4}{x+9}$

By the time Ananya and Gopika meet, Ananya would have travelled 48×x kms. After meeting, this is the distance that Gopika takes 9 hours to cover.

Hence, Gopika's speed =$\frac{48 x}{ 9}$ km/hr.

But we know that the ratio of Ananya's and Gopika's speeds are $1:\frac{x+4}{x+9}$

Therefore, $48:\frac{48x}{9} :: 1:\frac{x+4}{x+9}$

$\frac{x}{9}=\frac{x+4}{x+9}$

⇒$x^2+9x=9x+36$ ⇒$x^2=36 or x=6 hours.$

Hence, speed of Gopika =$\frac{48 x}{ 9}$

=$\frac{48 \times6}{ 9}$ = 32 kmph

1. Anil is rowing a boat. He takes twice the time in moving a certain distance upstream than downstream. What is the ratio of the rate of boat in still water to the rate of current?

Let speed in still water be x kmph

speed of current = y kmph

Downstream = x + y kmph

upstream = x - y kmph

Let the distance covered be a

From question,

$\frac{2a}{x+y} = \frac{a}{x-y}$

2(x-y) = x+y

x= 3y

x/y = 3/1

1. A train covers a journey of 4 stations connected to form a square at speeds of 20, 40, 60 and 80 km/hr. What is the average speed of train for this journey?

Speed = distance/time

Say, side of square = y km

time$\;t_1$ = y/20

$\;t_2$ = $\frac y{40}$, $\;t_3$ =$\frac y{60}$ and $\;t_4$ =$\frac y{80}$

Total time = $\frac{25y}{240}$

speed = total distance/total time

Required average speed = $\frac{4y}{t_1+t_2+t_3+t_4}$

= $\;\;\;\;\;\frac{4y\times240}{25y}$ = 38.4 km/hr.

1. A train covers a distance in 1 h 40 min, if it runs at a speed of 96 km/h on an average. Find the speed at which the train must run to reduce the time of journey to 1 h 20 min ?

Distance = $96\times\frac{100}{60} = 160 km$
New time = $\frac{80}{60} h = \frac{4}{3}h$
New speed = $160 \times\frac{3}{4} = 40\times 3 = 120kmph$