Respuesta :
SOLUTION:
In this question, we are given the following:
Kurt can ride his bike for 30 miles with the wind in the same amount of time that he goes 21 miles against the wind. If the wind's speed is 6 mph, what is Kurt’s speed on his bike?
Step 2:
The details of the solution are as follows:
Let Kurt's speed on the bike be U,
Kurt can ride his bike for 30 miles with the wind in the same amount of time,
If the wind's speed is 6 mph, it means that:
[tex](\text{ U+ 6 \rparen t = 30 -- equation 1}[/tex]
If he goes 21 miles against the wind and the wind's speed is 6 mph, it means that:
[tex](U-6)t\text{ = 21 --- equation 2}[/tex][tex]\begin{gathered} solving: \\ (U+6)t\text{ = 30 --equation 1} \\ (U-6)t\text{ = 21 --equation 2} \\ Divide\text{ equation 1 by equation 2, we have that:} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{(U+6)t\text{ }}{(U-6)t\text{ }}=\text{ }\frac{30}{21} \\ Then,\text{ we have that:} \\ 21\text{ \lparen U+6 \rparen = 30 \lparen U-6 \rparen} \\ 21U\text{ + 126 = 30 U -180} \\ collecting\text{ like terms, we have that:} \\ 126+\text{ 180 = 30 U -21 U} \\ 9U\text{ = 306} \\ Divide\text{ both sides by 9, we have that:} \\ U\text{ = }\frac{306}{9} \\ U\text{ = 34 miles per hour} \end{gathered}[/tex]CONCLUSION:
Kurt's speed on his bike = 34 miles per hour
