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X takes 3 hrs more than Y to walk 30 km. But, if X doubles his pace, he is ahead of Y by 1.5 hrs. What is their speed of walking?

2 Answers
Jun 19, 2018

Answer:

#v_x = 10/3#, #v_y = 5#

Explanation:

Assuming that both #X# and #Y# walk at constant speeds #v_x# and #v_y#, the time they need to walk #30#km is given by #t = 30/v#. The first sentence translates into

#30/v_x = 30/v_y+3 \qquad \qquad (1)#

In fact, the time it takes to #X# is #30/v_x#, and it is #3# more than the time it takes to #Y#, which is #30/v_y#.

As for the second sentence, if #X# doubles his speed he will pass from #v_x# to #2v_x#, and this time his time is #1.5# less than #Y#'s, thus translating into

#30/(2v_x) = 30/v_y-1.5 \qquad \qquad (2)#

We can solve the system by subtracting #(1)-(2)#, so that #Y#'s time simplifies: we have

#30/(v_x)-30/(2v_x) = (30/v_y+3)-(30/v_y-1.5)#

which can be written as

#cancel(30)^15/(cancel(2)v_x) = 15/v_x = 4.5#

solving for #v_x#, we have #v_x = 15/4.5 = 10/3#

Substitute this value for #v_x# in #(1)# to obtain #v_y#:

#30/(10/3) = 30/v_y+3 \iff 30*3/10 = 30/v_y+3 \iff 9=30/v_y+3#

which leads to #30/v_y = 6# and thus #v_y = 5#

Jun 19, 2018

Answer:

#"v"_"X" = 10/3\ "kmph"# and #"v"_"Y" = "5 kmph"#

Explanation:

Speed (#"v"#), distance (#"d"#) and time (#"t"#) are related as

#"v" = "d"/"t"#

For first case

#"v"_"X" = 30/"t"_"X" color(white)(..)# and #color(white)(..) "v"_"Y" = 30/"t"_"Y"#

It’s given that #"t"_"X" = "t"_"Y" + 3#

So, #"v"_"X" = 30/("t"_"Y" + 3) color(white)(...)# ——(1)

For second case

“X doubles his pace” means X doubles his speed. So speed of X now is #"2v"_"X"#

“X is ahead of Y by 1.5 hrs” means now X takes 1.5 hrs less than Y to travel same distance.
So, time tiken by X to travel 30 km is now #"t"_"Y" - 1.5#

#"2v"_"X" = 30/("t"_"Y" - 1.5)#

Substitute #"v"_"X"# from first equation

#2 × cancel(30)/("t"_"Y" + 3) = cancel(30)/("t"_"Y" - 1.5)#

#2/("t"_"Y" + 3) = 1/("t"_"Y" - 1.5)#

#"2t"_"Y" - 3.0 = "t"_"Y" + 3#

#color(blue)("t"_"Y" = 6)#

  • #"v"_"X" = 30/"t"_"X" = 30/("t"_"Y" + 3) = 30/(6 + 3) = 30/9 = 10/3#

  • #"v"_"Y" = 30/"t"_"Y" = 30/6 = 5#