What was the time for each runner in minutes and seconds?

Question

A German man and an Austrian woman claimed first place in

their respective divisions in the Empire State Building

Tower Race, a race up 86 flights of stairs – 1,576 steps in

all.

 Between the first- and second - place finishers in the

men’s and women’s divisions, the combined time of the

top four racers was 2,705 seconds.

 The second-place men’s finisher came in 17 seconds after

the men’s winner.

 The first–place woman’s time was 64 seconds longer than

the time of the men’s winner.

 The second–place women’s finisher took 84 seconds longer

than the women’s champion.

What was the time for each runner in minutes and seconds?

Answer 1

Hi Nancy,

 

This is a 4 equations in 4 unknowns problem. Let's assume:

 

fm = first man time

sm = second man time

fw = first woman time

sw = second woman time

 

 

fm+sm+fw+sw = 2705 --> EQ1

fm = sm-17 --> EQ2 (or sm = fm+17)

fm = fw-64 --> EQ3 (or fw = fm+64)

fw = sw-84 -->EQ4 

 

from equations 3 and 4

fm = (sw-84) - 64 = sw-148 --> EQ5 (or sw=fm+148)

 

use equations 2,3 & 5 and substitute in equation 1 as follows

fm + (fm+17) + (fm+64) + (fm+148) = 2705

4fm = 2476

fm = 619 seconds

sm = fm + 17 = 636 seconds

fw = fm + 64 =  683 seconds

sw = fm+ 148 = 767 seconds

 

good luck