Two bells ring at intervals of 30 minutes and 40 minutes respectively. a) After how many minutes will they…

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Two bells ring at intervals of 30 minutes and 40 minutes respectively. a) After how many minutes will they ring together? b) If they rang at 11:00 am, at what time will they ring together again?

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Here are the solutions to problems 26 and 27. cannot be solved as the necessary diagram is not provided.

: Two bells ring at intervals of 30 minutes and 40 minutes respectively.

a) After how many minutes will they ring together?

Find the Least Common Multiple (LCM) of 30 and 40.
We can use prime factorization:
$30 = 2 \times 3 \times 5$ $40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5$
The LCM is found by taking the highest power of each prime factor present in either number:
$\text{LCM}(30, 40) = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120$
The bells will ring together after $\boxed{\text{120 minutes}}$ .

b) If they rang at 11:00 am, at what time will they ring together again?
Convert the LCM from minutes to hours.
$120 \text{ minutes} = \frac{120}{60} \text{ hours} = 2 \text{ hours}$
Add the time interval to the given time.
The bells rang at 11:00 am. They will ring together again after 2 hours.
$11:00 \text{ am} + 2 \text{ hours} = 1:00 \text{ pm}$
They will ring together again at $\boxed{\text{1:00 pm}}$ .

: A motorist left Kampala for Masaka at a speed of $48 \text{ km/hr}$ at $8:30 \text{ am}$ and spent $2\frac{1}{2} \text{ hr}$ on the journey.

a) At what time did the motorist reach Masaka?
Identify the departure time and travel time.
Departure time = $8:30 \text{ am}$
Travel time = $2\frac{1}{2} \text{ hours} = 2 \text{ hours and } 30 \text{ minutes}$
Add the travel time to the departure time.
$8:30 \text{ am} + 2 \text{ hours } 30 \text{ minutes}$
Adding 2 hours to 8:30 am gives 10:30 am.
Adding 30 minutes to 10:30 am gives 11:00 am.
The motorist reached Masaka at $\boxed{\text{11:00 am}}$ .

b) Calculate the distance the motorist covered from Kampala to Masaka?
Identify the speed and time.
Speed = $48 \text{ km/hr}$
Time = $2\frac{1}{2} \text{ hours} = 2.5 \text{ hours}$
Use the formula Distance = Speed $\times$ Time.
$\text{Distance} = 48 \text{ km/hr} \times 2.5 \text{ hr}$ $\text{Distance} = 48 \times \frac{5}{2} \text{ km}$ $\text{Distance} = 24 \times 5 \text{ km}$ $\text{Distance} = 120 \text{ km}$
The distance covered is $\boxed{\text{120 km}}$ .

Two bells ring at intervals of 30 minutes and 40 minutes respectively. a) After how many minutes will they ring together? b) If they rang at 11:00 am, at what time will they ring together again?

Step-by-step solution

Find the Least Common Multiple (LCM) of 30 and 40.

Convert the LCM from minutes to hours.

Add the time interval to the given time.

Identify the departure time and travel time.

Add the travel time to the departure time.

Identify the speed and time.

Use the formula Distance = Speed $\times$ Time.

Still stuck on this one?

More Mathematics Questions

Two bells ring at intervals of 30 minutes and 40 minutes respectively. a) After how many minutes will they ring together? b) If they rang at 11:00 am, at what time will they ring together again?

Step-by-step solution

Find the Least Common Multiple (LCM) of 30 and 40.

Convert the LCM from minutes to hours.

Add the time interval to the given time.

Identify the departure time and travel time.

Add the travel time to the departure time.

Identify the speed and time.

Use the formula Distance = Speed ×\times× Time.

Still stuck on this one?

More Mathematics Questions

Use the formula Distance = Speed $\times$ Time.