Time and distance

6.

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
A.     1 hour    B.     2 hours
C.     3 hours    D.     4 hours
Answer & Explanation

Answer: Option A

Explanation:

Let the duration of the flight be x hours.

Then,     600     –     600     = 200
x     x + (1/2)

600     –     1200     = 200
x     2x + 1

x(2x + 1) = 3

2×2 + x – 3 = 0

(2x + 3)(x – 1) = 0

x = 1 hr.      [neglecting the -ve value of x]

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7.

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
A.     220 km    B.     224 km
C.     230 km    D.     234 km
Answer & Explanation

Answer: Option B

Explanation:

(1/2)x     +     (1/2)x     = 10
21     24

x     +     x     = 20
21     24

15x = 168 x 20

x =         168 x 20         = 224 km.
15

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8.

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
A.     70 km/hr    B.     75 km/hr
C.     84 km/hr    D.     87.5 km/hr
Answer & Explanation

Answer: Option D

Explanation:

Let the speed of two trains be 7x and 8x km/hr.

Then, 8x =         400         = 100
4

x =         100         = 12.5
8

Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

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9.

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
A.     35.55 km/hr    B.     36 km/hr
C.     71.11 km/hr    D.     71 km/hr
Answer & Explanation

Answer: Option C

Explanation:

Total time taken =         160     +     160     hrs.     =     9     hrs.
64     80     2

Average speed =         320 x     2     km/hr     = 71.11 km/hr.
9

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10.

A car travelling with of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
A.
17     6     km/hr
7
B.     25 km/hr
C.     30 km/hr    D.     35 km/hr
Answer & Explanation

Answer: Option D

Explanation:

Time taken = 1 hr 40 min 48 sec = 1 hr 40     4     min = 1     51     hrs =     126     hrs.
5     75     75

Let the actual speed be x km/hr.

Then,     5     x x     126     = 42
7     75

x =         42 x 7 x 75         = 35 km/hr.