Which one is faster?

Algebra Level pending

Harry can swim from point A A to point B B (with the current) in 40 m i n 40min and from B B to A A ( against the current) in 45 m i n 45min .

how long does it take him to row from A A to B B if he row from B B to A A in 15 m i n 15min ?

if the answer is for example 12 m i n 12min and 21 s e c o n d s 21seconds write it as 1221 1221

(Assume that the speed of the current and Harry’s swimming and rowing speeds relative to the current are all constant.)


The answer is 1424.

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2 solutions

Chew-Seong Cheong
Jul 16, 2015

Let the distance between A A and B B be d d , the river flow, Harry's swimming and rolling speeds be v 0 v_0 , v 1 v_1 and v 2 v_2 respectively, and the time for Harry to row from A A to B B be t t . The we have:

{ 40 ( v 1 + v 0 ) = d v 1 + v 0 = d 40 . . . ( 1 ) 45 ( v 1 v 0 ) = d v 1 v 0 = d 45 . . . ( 2 ) 15 ( v 2 v 0 ) = d v 2 v 0 = d 15 . . . ( 3 ) t ( v 2 + v 0 ) = d . . . ( 4 ) \begin{cases} 40(v_1+v_0) = d & \Rightarrow v_1+v_0 = \dfrac{d}{40} &...(1) \\ 45(v_1-v_0) = d & \Rightarrow v_1-v_0 = \dfrac{d}{45} &...(2) \\ 15(v_2-v_0) = d & \Rightarrow v_2-v_0 = \dfrac{d}{15} &...(3) \\ \space \space t\space (v_2+v_0) = d & &...(4) \end{cases}

{ ( 1 ) ( 2 ) : 2 v 0 = ( 1 40 1 45 ) d v 0 = d 720 ( 3 ) : v 2 d 720 = d 15 v 2 = 49 d 720 ( 4 ) : t ( 49 d 720 + d 720 ) = d t = 720 50 = 14.4 = 14 : 24 \begin{cases} (1)-(2): & 2v_0 = \left(\dfrac{1}{40} - \dfrac{1}{45} \right) d & \Rightarrow v_0 = \dfrac{d}{720} \\ (3): & v_2 - \dfrac{d}{720} = \dfrac{d}{15} & \Rightarrow v_2 = \dfrac{49d}{720} \\ (4): & t \left(\dfrac{49d}{720} + \dfrac{d}{720} \right) = d & \Rightarrow t = \dfrac{720}{50} = 14.4 = 14:24 \end{cases}

Therefore, the required answer is 1424 \boxed{1424} .

Abdeslem Smahi
Jul 16, 2015

Let the distance from A A to B B is 1 1 , and let x , y , z x,y,z be the the speeds of the current and Harry's swimming and rowing, respectively. Then

y + x = 1 45 = 9 360 y+x=\frac{1}{45}=\frac{9}{360} and y x = 1 45 = 8 360 y-x=\frac{1}{45}=\frac{8}{360} and z x = 1 15 = 24 360 z-x=\frac{1}{15}=\frac{24}{360}

so

z + x = ( y + x ) ( y x ) + ( z x ) = 9 8 + 24 360 = 25 360 z+x=(y+x)-(y-x)+(z-x)=\frac{9-8+24}{360}=\frac{25}{360}

so it take harry 360 24 = 14.4 m i n \frac{360}{24}=14.4min to row from A A to B B

which mean 14 m i n 14min and 24 s e c o n d s 24seconds

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