Question

2. Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four
minutes later Christen joined him and peeled at the rate of 5 potatoes per minute.
When they finished, how many potatoes had Christen peeled?​

Answer 1

The potatoes that Christen peeled is 20.

Step-by-step explanation:

Again, I will use the "rate" method.

• Rate of Homer = 3 potatoes per minute, i.e., 3/1.
• Rate of christen = 5 potatoes per minute, i.e., 5/1

Homer started peeling 44 potatoes at the rate of 3 potatoes per minute.

Therefore he will peel 3 × 4 = 12 potatoes in 4 minutes.

So now there are 44 - 12 = 32 potatoes left.

Christen joined him at the rate of 5 potatoes per minute.

And now Homer is as usual peeling 3 potatoes per minute.

Together they will peel 8 potatoes per minute.

Then they will peel 8 × 4 = 32 potatoes at 4 minutes.

Conclusion - they require 4 minutes to peel 32 potatoes.

Required answer:

Number of potatoes = Rate of Christian × time.

= (5/1) × 4

= 20 potatoes.

- Therefore Christian peeled 20 potatoes.

Answer 2

$\large\underline{\underline{\bold{\pink{\mathfrak{ANswER}}}}}$

$\large\underline\bold{GIVEN,}$

$\dashrightarrow \: \rm{ \red{ Homer :-}}peeling\:44\:potatoes\:at\:the\:rage\:of\: \\ 3\: potatoes\:permin\\ \dashrightarrow \rm{\pink{christen:-}}he\:peeled\:5\:potatoes\:at\:the\:rate\: \\ of5\: potatoes\:per \:minute. \\ \large{\red{TAKING\:CONCLUSION\:OF\:44\: POTATOES \:}} \\ \rm{ \star\:\: Homer \:rate:- \dfrac{3}{1} potatoes/per\:min } \\ \red{note:- \text{ after four min christen join him so in four min how many potatoes he peeled=}} \\ \dashrightarrow \dfrac{3}{1} \times 4 \\ \implies 12 \\ \large{\underline{ \red{boxed{Homer\:peeled\:12\: potatoes\:in\:last\:4\:min }}}}$

$\large\underline\bold{TO\:FIND,}$

$\therefore how\:many\:potatoes\:did\:christian\:peeled.$

$\large\underline{\underline{\bold{\pink{\mathfrak{SOLUTION}}}}}$

$\therefore We\:know\\ \therefore in\:last\:4\:min(before\:christian\:join\:with\:homer\:in\:peeling\:of\:potatoes\: \\ homer\: peeled\: 12\: potatoes \\ \therefore \:potatoes\:left\:to\:peel\: by\:christen\:is\: \\ \implies 44-12= 32 \\ \boxed{\red{ 32\:potatoes\:left\:to\:peel\:out.}} \\ \therefore\: they\:started\:both\:together\:peeling\:at\: 32\:potatoes\: \\ Now\:taking \: a minute ahead\\ \therefore \: as\:given \: in \:a minute \: homer \:can\:peel\: 3\:potatoes \: \\ \therefore \: 32-3 = 29 \\ \therefore \:in\:other\: side \:christian \: can \: peel\: 5\:potatoes\:in\:a\:min \\ \therefore 29-5= 24 \\ \dashrightarrow 24\:potatoes \:left \: \\ continuing \:like \:these \: for another 3\:min \: \\ \therefore homer:- 24-(3\times 3)= 24-9= 15 \\ whereas\: \\ \therefore 15- (5\times 3)= 15-15=0 \\ \therefore \:atlast\: 0\:potatoes(all\:potatoes \:overed\: ) \\ \large{\purple{counting \:the\:potatoes \:peeled\:by\:christen}} \\ \dashrightarrow in\:first\:moment\: he\:peeled\:t\:potatoes \\ \therefore in\:second\:moment\:of\:3\:min\: he\:peeled\: 15\: potatoes\: \\ \therefore \:adding\: both\: moments\: we\: get, \\ \implies 5+15 \\ \implies 20 \\ \large{\underline{\red{\boxed{20\:potatoes\:peeled\:by\:christen.}}}}$

$\large\underline\bold{\star\:\: 20\:POTATOES\:WERE\:PEELED\:BY\:CHRISTEN. \checkmark}$

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