# Combined Rates YouTube Lecture Handouts

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If Rajesh can build a house in 2 days and his apprentice can build a house in 3 days, then working together, how long will it take them to build the house.

A certain number of small parts need to be produced. 30 parts are scheduled to be produced after each day. After 1/3 of the parts are produced, the rate of production increases by 10 % thanks to improvement on efficiency. It takes 4 fewer days to produce all the parts than scheduled. How many parts are in total?

If Rajesh can build **a house in 2 days** and his apprentice can build **a house in 3 days**, then working together, how long will it take them to build the house.

Student A writes **2 essays each hour**. Student B writes **3 essays each hour**. If they worked together without interfering each other, how long does it take to finish 1 essay

A and B can do a given work in 12 and 18 days respectively. They work alternately for equal period of time. And A started the work. Now, what is the time taken by A and B to complete the job

A project can be done by **70 men in 100 days**. There were **80 men** at the start of the project but after **50 days**, 20 of them had to be transferred to another project. How long will it take the remaining workforce to complete the job. (EFFORT)

8 men can complete a piece of work in 20 days. 8 women can do the same work in 32 days. In how many days will 5 men and 8 women together will complete the same work.

An experienced bricklayer can work twice as fast as an apprentice bricklayer. After the bricklayers work together on a job for 6 hrs, the experienced bricklayer quits. The apprentice requires 12 more hours to finish the job. How long would it take the experienced bricklayer, working alone, to do the job?

A and B working together can finish painting a home in six days. A working alone can finish it in 5 days less than B. How long will it take each of them to finish the work alone

Working continuously at its constant rate, machine A takes 3 hours to produce a batch of computer parts. Working continuously at its constant rate, machine B takes 2 hours to produce an identical batch of parts. If in reality machine A needs repairs of 1 min every 10 min and machine B needs break of 2 min every 30 min, how long will it take the two machines to produce the same batch of parts.

A certain number of small parts need to be produced. 30 parts are scheduled to be produced after each day. After 1/3 of the parts are produced, the rate of production increases by 10 % thanks to improvement on efficiency. It takes 4 fewer days to produce all the parts than scheduled. How many parts are in total?

**Next Class (Piper and Cisterns)** : Two pipes A and B fill a tank in 20 minutes and 40 minutes respectively. A pipe C at the bottom can empty the tank in 60 minutes. If all three pipes were open simultaneously, how long does it take to fill the empty tank? **Further Ahead (Races, Head Start, Dead Heat)** : In a 2000m race between A and B. A gives B a start of a minute but still beats him by 200 m . When he increases the head start to 80 seconds , the race ends in dead heat. Find the speed of A.

✍ Mayank