Two tourists left two towns simultaneously, the distance between which is 38 km, and met in 4 hours. What was the speed of each of the tourists, if the first one covered 2 km more than the second one before they met?
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"Suppose that I don't have a formula for #g(x)# but I know that #g(1)
= 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
#=>v_1 =5 "km"/"hr"#
#=>v_2 = 4.5 "km"/"hr"#
Let #d_1# and #d_2# be the distances traveled in #"km"# by each of the tourists.
We can write the total distance traveled as:
#d_"tot" = d_1 + d_2 = 38#
We are told directly that the first tourist travels more than the second tourist:
#d_1 = d_2 + 2#
We use these two equations to find the distance each tourist covered.
#(d_2 + 2) + d_2 = 38#
#2d_2 + 2 = 38#
#d_2 + 1 = 19#
#d_2 = 18#
Substituting back to find #d_1#:
#d_1 = d_2 + 2 = 18+2 = 20#
So we have found #d_1 = 20 " km"# and #d_2 = 18 " km"#.
We know that each tourist traveled for #t = 4 " hr"#. Velocity is defined as distance per unit time, so we can compute the velocities using the time and distances we found earlier.
#v_1 = d_1/ t = 20/4 = color(blue)(5 "km"/"hr")#
#v_2 = d_2/t = 18/4 = color(blue)(4.5 "km"/"hr")#
