Question

the angle between the two hands of a clock is 70degrees when the hour hand is between 7 and 8.what time does the watch show?

Answer 1

As the angle at the centre is 360
Then angle at each hour = 30 degree
The Time will be 7:46

Answer 2

Given: The angle between the two hands of a clock is 70°

Find: What time will the watch show, once the hand is between seven and eight.

Solution:

We know that In hr, minute hand covers 360 degrees.

Hour hand covers 30 degrees. In every 60 Min Minute hand covers 330 degrees over the hour hand.

330 degree in minutes = 55 Minutes

So, we can conclude that in every 60 Minute Minute hand is 55 Minute ahead.

To be 1 minute ahead, time taken by minute hand =60/55

                                                                                   =12/11

Situation 1- Once the minute hand is behind

The distance while there will be time 7 'o' clock = 35 minutes or 210° Distance to be cover to make 70 degrees =210-70

                                                                      =140° or 70/3 min.

time taken after 7=70/3x12/11

                             =25 (5/11)

So, the exact time when the hands will be together=7:25

Situation-2 When the minute hand is ahead

The distance while there will be time 7 'o' clock=35 minutes or 210°

Distance to be cover to make 70°=210+70

                                                       =280° or 140/3 min

Time taken after 7=140/3x12/11

                             =50(10/11)

So the exact time when the hands will be together = 7: 50

Final answer: 7:25 or 7:50

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