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GMAT Quant — Applied Mathematics (Word Problems)

Two ropes, Rope P and Rope Q, each have the same initial length, but Rope P burns completely in m minutes while Rope Q burns completely in 4 m minutes. They are lit simultaneously at one end. In terms of m, after how many minutes will the remaining length of Rope Q be twice the remaining length of Rope P?

Explanation	Calculations	Help
$We let L be the initial length of each rope and let t be the elapsed time in minutes.$	$L = initial length of each rope t = elapsed time in minutes$
$We express the remaining length of each rope based on its constant burn rate.$	$Remaining length of P = L - \frac{L}{m} t Remaining length of Q = L - \frac{L}{4 m} t$	Theory & Tactics Method Card RATE1-C Click to view full details
$We set up the equation for "remaining length of Rope Q be twice the remaining length of Rope P" .$	$L - \frac{L}{4 m} t = 2 (L - \frac{L}{m} t)$
$We solve the equation by dividing out L, clearing denominators, grouping like terms, and isolating t .$	$\text{Rearrange terms:$	Theory & Tactics Method Card EQUA1-C Click to view full details

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C

GMAT Quant — Applied Mathematics (Word Problems)

Two ropes, Rope P and Rope Q, each have the same initial length, but Rope P burns completely in m minutes while Rope Q burns completely in 4 m minutes. They are lit simultaneously at one end. In terms of m, after how many minutes will the remaining length of Rope Q be twice the remaining length of Rope P?

Explanation	Calculations	Help
$We let L be the initial length of each rope and let t be the elapsed time in minutes.$	$L = initial length of each rope t = elapsed time in minutes$
$We express the remaining length of each rope based on its constant burn rate.$	$Remaining length of P = L - \frac{L}{m} t Remaining length of Q = L - \frac{L}{4 m} t$	Theory & Tactics Method Card RATE1-C Click to view full details
$We set up the equation for "remaining length of Rope Q be twice the remaining length of Rope P" .$	$L - \frac{L}{4 m} t = 2 (L - \frac{L}{m} t)$
$We solve the equation by dividing out L, clearing denominators, grouping like terms, and isolating t .$	$\text{Rearrange terms:$	Theory & Tactics Method Card EQUA1-C Click to view full details

Scroll horizontally to view all columns

C