#speeddistancetime

[num8ers]

[logicxonomy]

Movement in Opposite directions (Speed Distance and Time)

Que: Two persons A and B start moving toward each other just after A has fired. After 10 minutes A fired again. The time between which B hears these two shots is 9 minutes. If the speed of A is 18 km/h, then find the speed of B. The speed of sound is given as 1080 km/hr.

(a) 120 km/h

(b) 100 km/h

(c) 96 km/h

(d) 84 km/h

Solution: In 10 minutes A covered ⇒ Speed×Time= (10/60)×18 = 3 km

Time taken by sound to cover this 3 km= 3000/300= 10 sec

This means that if B does not move, he will hear the gunshot in 9 minutes and 50 seconds.

Note: 10 min- 10 sec= 9 min 50 sec

B heard the gunshot after 9 minutes. So the travel time of B is 9 minutes and the travel time of sound from the new position of B to the original position of B is 50 seconds.

Note: 9 min 50 sec- 9 min= 50 sec

Distance covered by B in 9 min= Distance covered by sound in 50 sec

k×(9×60)= 300×50

k=250/9 m/sec

k= (250/9)×(18/5)= 100 km/h

Here k is the speed of B.

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[logicxonomy]

Find the distance between P and Q

Que: Rohan and Sohan are at points A and B respectively which are 126 km apart, start driving toward each other and meet at point P. After reaching B and A respectively they start back to their previous position and in the meantime meet at point Q. Find the distance between P and Q if Rohan takes 9 hours from P to B and Sohan takes 16 hours from P to A?

(a) 22.4 km

(b) 24 km

(c) 36 km

(d) 40 km

Solution: Let, the speeds of Rohan and Sohan are x and y respectively

Time taken by Rohan from P to B (t₁)= 9 hr

Time taken by Sohan from P to A (t₂)= 16 hr

x/y=√(t₂/t₁)

x:y= 4:3

Let, x=4k and y=3k

Time taken by both to reach P (First meeting)= t=√(t₁×t₂)=12 hr

Total time taken by Rohan to complete the journey from A to B= 12+9=21 hr

Distance AB= Speed of Rohan ×Time= 4k ×21=84k

Note: 84k=126 km (Given)

Total time taken for the second meeting= Distance/Relative Speed= (3×84k)/7k= 36 hr

Since Sohan takes 28 hours from B to A so for the second meeting at Q, he has to cover 8 hr journey.

Distance between A to Q= Speed of Sohan×Time= 3k×8= 24k

Distance between A to P= Speed of Rohan×Time= 4k×12= 48k

PQ=AP-AQ= 24k

Given, 84k= 126

So, 24k= 36 km

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[logicxonomy]

Find the original speed of the car

Que: Rohan started his journey from A to B by car. If he takes a lunch break of 15 minutes in a restaurant at a distance of 80 km from A in the middle of the journey and then proceeds at 16.67% slower speed, he will reach the destination 90 minutes late and if he takes this lunch break 60 km further on, he will reach 75 min late. Find the original speed of the car.

(a) 56 kmph

(b) 50 kmph

(c) 48 kmph

(d) 40 kmph

Solution: 16.67%=1/6

Let, the initial speed be 6x. So, the reduced speed is 5x

Case 1: At the first restaurant(C)

Speed⇒ 6:5

Time⇒ 5:6

Time difference= 1 unit= 75 min

Note: Exclude the lunchtime of 15 min

The original time taken to cover the journey from C to B=5 unit=5×75= 375 min

Case 2: At the second restaurant(D)

Speed⇒ 6:5

Time⇒ 5:6

Time difference= 1 unit= 60 min

Note: Exclude the lunchtime of 15 min

The original time taken to cover the journey from D to B=5 unit=5×60= 300 min

Time taken to cover the journey from C to D= 375–300= 75 min= 75/60=5/4 hr

The original speed= 60/(5/4) =48 kmph

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[arithmeticcalculator]

Speed Distance Time Calculator | How to find Time Speed and Distance?

Speed Distance Calculator calculates the Time Speed and Distance values if any two parameters are given as inputs. Check Time, Speed & Distance Formulae.