AMCAT Speed, Time and Distance Quiz-3

Correct Option: 6 km
Let the distance be x and the difference between time taken = 25 - (-25) = 50 mins = 5/6 hr.
Time taken when traveled at 4 km/hr (slower) – Time taken when traveled at 9 km/hr (faster) = Difference in time = 5/6 hr
\frac{x}{4}-\frac{x}{9} =\frac{5}{6}
\frac{9x-4x}{36}=\frac{5}{6}
5x=\frac{5}{6}\times36
x = 6 km

Ans:
(8 – x)=(10 – 2x)
=> x = 2 Hours

Explanation -Let the Distance between home and office =d. Suppose he reaches the office on Time, the Time taken = x minutes
Case 1: When he reaches office 20 minutes late,
Time taken = x+20
Case 2: when he reaches office 10 minutes early,
Time taken = x-10 As the Distance traveled is the same, the ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases Ratio of Speed in both cases = 4:6 = 2:3 Ratio of Time in both cases = 3:2 Therefore (x+20)/(x-10)=3/2 2x+40 = 3x -30 x= 70 minutes Taking case 1, 4= d/(90/60)=> d= 360/60 = 6 km

Explanation:
As the Distance covered is same with both the Speeds, the average Speed will be the harmonic mean
of the individual Speed.
\frac{200}{9 } \frac{m}{s} = \frac{(200*3600)}{((9*1000) ) } = 80 \frac{km}{h}
So, average Speed = \frac{(2*a*b)}{(a + b)}
= \frac{(2 * 80 * 120)}{(80 + 120) }= 96 \frac{km}{h}

Answer: 7.2

Explanation:
Speed = 600 m/ 300 sec. = 2 m/sec. = 2 x 18/5km/hr =7.2 km/hr

Explanation- Suppose the Speed of the river is ‘y’ kmph.
While rowing upstream he takes 2 hrs and while rowing downstream he takes 1 & Half hours.
As the Distance covered is constant the ratio of the net Speeds of the boat while going upstream and downstream will be the inverse of the ratio of the Time taken.
Ratio of Time taken (downstream: upstream) = 1.5/2 = 3 / 4
So the ratio of Speed of boat (downstream: upstream) = 4/3
Speed downstream: 10 + y Speed upstream : 10 – y
\frac{10+y}{10-y}=\frac{4}{3}
30+3y=40-4y. Thus, 7y=10 & Y=10/7
Speed of river = 10/7 kmph

Distance = Speed* Time
As Distance covered in both the cases is constant, Speed will be inversely proportional to time.
So, if Time by bus: Time by train = 2: 1, Speed of bus: Speed of train = 1: 2
Speed of bus is 40 \frac{km}{h}, so Speed of train is 80 \frac{km}{h}

Answer: 720 km/hr

Explanation:

Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed=\frac{1200}{\frac{5}{3}}

Speed=1200\times \frac{5}{3}=720 km/h

Correct Option: 40 min
Let the distance be x, then,

(Time taken to walk x km) + (Time taken to ride x km) = 58 min.

⇒ (Time taken to walk 2x km) + (Time taken to ride 2x km) = 116 min.

But, time taken to walk both ways 2x km = 76 min.

So, Time to ride 2x km = (116 - 76) min ⇒ 40 min.

Explanation- We are given that two thirds of the 6 km was covered at 4 km / hr i.e. 4 km distance was covered at 4 km / hr. Time taken to cover 4 km = 4 km / 4 km / hr = 1 hr = 60 minutes
Time left = 84 – 60 = 24 minutes
Now, the man has to cover remaining 2 km in 24 minutes or 24 / 60 = 0.4 hours
Speed required for remaining 2 km = 2 km / 0.4 hr = 5 km / hr