It is 1:50PM. What is the sum of the degrees the minute and hour hands of a clock will rotate between now and when it hits 2:15PM?

162.5°

Step-by-step explanation:

1. Calculate the number of minutes

(a) Subtract the hours and the minutes separately

2: 15

-1: 50

1: - 35

(ii) If the minutes are negative, subtract 1 from the hours and add 60 to the minutes.

1: - 35

-1: + 60

0: 25

The clock has been running for 25 min.

2. Calculate the travel of the minute hand (θm)

The clock face is a circle of 360°, and there are 60 min in 1 h,

so, the minute hand travels 6° in 1 min.

In 25 min, the minute hand will travel

θm = 25 * 6 = 150°

3. Calculate the travel of the hour hand (θh)

The hour hand travels 360° in 12 h, so it travels 30° in 1 h and 0.5° in 1 min.

It has travelled for 25 min.

θh = 25 * 0.5 = 12.5°

4. Calculate the sum of the angles

θm + θh = 150° + 12.5° = 162.5°