Time Speed Distance

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Speed Time And Distance

Question 1 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
A
3 : 4
B
4 : 3
C
2 : 3
D
3 : 2
Question 1 Explanation: 
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{speed}}\, {\text{of}}\, {\text{the}}\, {\text{train}}\, {\text{be}}\, x\, {\text{km/hr}} \cr & {\text{and}}\, {\text{that}}\, {\text{of}}\, {\text{the}}\, {\text{car}}\, {\text{be}}\, y\, {\text{km/hr}} \cr & {\text{Then}}, \, \frac{{120}}{x} + \frac{{480}}{y} = 8 \cr & \Rightarrow \frac{1}{x} + \frac{4}{y} = \frac{1}{{15}}\, .....\left( i \right) \cr & {\text{and}}, \, \frac{{200}}{x} + \frac{{400}}{y} = \frac{{25}}{3} \cr & \Rightarrow \frac{1}{x} + \frac{2}{y} = \frac{1}{{24}}\, .....\left( {ii} \right) \cr & {\text{Solving}}\, \left( {\text{i}} \right)\, {\text{and}}\, \left( {{\text{ii}}} \right){\text{, }}\, \cr & {\text{we}}\, {\text{get}}, \, x = 60\, {\text{and}}\, y = 80 \cr & \therefore {\text{Ratio}}\, {\text{of}}\, {\text{speeds}} \cr & = 60:80 = 3:4 \cr\end{align}
Question 2 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A car after traveling 18 km from a point A developed some problem in the engine and the speed became 4/5th of its original speed. As a result, the car reached point B 45 minutes late. If the engine had developed the same problem after traveling 30 km from A, then it would have reached 36 minutes late. The original speed of the car (in km/h) is:
A
25
B
35
C
20
D
30
Question 2 Explanation: 
He proceeds at 4/5 S where S is his usual speed means 1/5 decrease in speed which will lead to 1/4 increase in time. Now the main difference comes in those 12km (30-18) and the change in difference of time = (45-36) min = 9 min

Thus,

1/4 * T = 9 min where T is the time required to cover the distance of (30 - 18) = 12 km

T = 36 min = 36/60 hours = 0.6 hours.

Speed of the car = 12/0.6 = 20 kmph.

Question 3 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:
A
15 km
B
16 km
C
14 km
D
17 km
Question 3 Explanation: 
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{distance}}\, {\text{travelled}}\, {\text{on}}\, {\text{foot}}\, {\text{be}}\, x\, km \cr & {\text{Then, }}\, {\text{distance}}\, {\text{travelled}}\, {\text{on}}\, {\text{bicycle}} = \left( {61 - x} \right)km \cr & {\text{So}}, \, \frac{x}{4} + \frac{{\left( {61 - x} \right)}}{9} = 9 \cr & \Rightarrow 9x + 4\left( {61 - x} \right) = 9 \times 36 \cr & \Rightarrow 5x = 80 \cr & \Rightarrow x = 16\, km \cr\end{align}
Question 4 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
A
12 kmph
B
11 kmph
C
14 kmph
D
8 kmph
Question 4 Explanation: 
\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{distance}}\, {\text{travelled}}\, {\text{by}}\, x\, {\text{km}} \cr & {\text{Then}}, \, \frac{x}{{10}} - \frac{x}{{15}} = 2 \cr & \Rightarrow 3x - 2x = 60 \cr & \Rightarrow x = 60\, km \cr & {\text{Time}}\, {\text{taken}}\, {\text{to}}\, {\text{travel}}\, 60\, km\, {\text{at}}\, 10\, {\text{km/hr}} \cr & = \left( {\frac{{60}}{{10}}} \right)\, hrs = 6\, hrs \cr & {\text{So, }}\, {\text{Robert}}\, {\text{started}}\, {\text{6}}\, {\text{hours}}\, {\text{before}}\, 2\, P.M.\, i.e., \, at\, A.M. \cr & \therefore {\text{Required}}\, {\text{speed}} \cr & = \left( {\frac{{60}}{5}} \right)\, kmph = 12\, kmph \cr\end{align}
Question 5 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A motor car does a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey?
A
624 km
B
600 km
C
584 km
D
684 km
Question 5 Explanation: 
Let the total distance be 2X.

A.....X km.....M.....X km.....B

Total time taken in the journey = 17.5 hours

Time taken to cover X km at 30 km/h = X/30.

Time taken to cover X km at 40 km/h = X/40

Now, \begin{align} & \left( {\frac{X}{{30}}} \right) + \left( {\frac{X}{{40}}} \right) = 17.5 \cr & \left[ {\frac{{\left( {40X + 30X} \right)}}{{1200}}} \right] = 17.5 \cr & 70X = 17.5 \times 1200 \cr & X = 300\, km \cr & {\text{Total}}\, {\text{distance}}, \, 2x \cr & = 600\, km \cr\end{align}

There are 5 questions to complete.

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