Given:
a.) Manuel can drive 5 times as fast as Carlos can ride his bicycle.
b.) It takes Carlos 3 hours longer than Manuel to travel 60 miles.
Solution:
Let,
x = Carlos' speed
y = Manuel's speed
Manuel can drive 5 times as fast as Carlos can ride his bicycle.
[tex]\text{ y = 5x}[/tex][tex]\text{ x = }\frac{\text{Distance}}{\text{ Time}}=\frac{\text{ 60}}{\text{ T + 3}}\text{ ; T = Time of Manuel to reach miles}[/tex][tex]\text{ y = }\frac{\text{60}}{\text{ T}}\text{ }\rightarrow\text{ 5x =}\frac{\text{ 60}}{\text{ T}}\text{ }\rightarrow\text{ x =}\frac{\text{60}}{\text{ 5T}}[/tex]Let's incorporate the formula for Manuel and Carlos' speed to find T.
[tex]\frac{\text{ 60}}{\text{ T + 3}}=\frac{\text{ 60}}{\text{ 5T}}[/tex][tex]\begin{gathered} \text{ \lparen60\rparen\lparen5T\rparen = \lparen60\rparen\lparen T + 3\rparen} \\ \text{ 300T = 60T + 180} \\ \text{ 300T - 60T = 180} \\ \text{ 240T = 180} \\ \text{ 240T/240 = 180/240 } \\ \text{ T = 180/240 = 3/4 or 0.75 hours} \end{gathered}[/tex][tex]\text{ 0.75 hours x 60 mins/hour = 45 mins.}[/tex]Therefore,
Manuel can travel 60 miles in 45 mins. while Carlos can travel 60 miles in 3 hours and 45 minutes.
Let's determine the speed of Carlos,
[tex]\text{ x = Speed = Distance/Time}[/tex][tex]\text{ = 60 miles/3.75 hours}[/tex][tex]\text{ Speed = 16 miles per hour \lparen mph\rparen}[/tex]Therefore, Carlos' speed is 16 mph.
