Question

Doctor Jones starts an appointment every 20 minutes.
Doctor Warholm starts an appointment every 35 minutes.
The first appointment for both doctors starts at 8.30 am.
What is the next time that they have an appointment start at the same time?

Answer 1

Given:

The first appointment for both doctors starts at 8:30am.

To find:

Next appointment that they start at same time.

Solution:

For the same time same time take LCM of 20 and 35.

20= 2x2x5

35= 5×7

hcm (20,35) = 2X2X5X7 = 140

They will take appointment after 140 minutes. 1.e. 2 hours 20 minute.

so, next appoitment will be 10:50a.m.

Answer 2

The next time that they have an appointment start at the same time is at  10:50 a.m.

How do we calculate the appointment time start?

We are given that the first appointment for both doctors starts at 8:30am while the Next appointment also started at same time but Doctor Jones starts his every 20 minutes while Doctor Warholm starts his every 35 minutes.

First step

For the same time, take LCM of 20 and 35.

20 = 2 * 2 * 5

35 = 5 * 7

Second step

HCM (20, 35) = 2 * 2 * 5 * 7

HCM (20, 35) = 140

Hence, it will take the appointment after 140 minutes which equals to 2 hours 20 minute.

Now, from 8.30 am, the addition of the 2 hours 20 minute gives us 10:50 a.m which is the next time that they have an appointment start at the same time.

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