Respuesta :
Step 1: Assign variable for the unknown that you need to find.
[tex] d_w \; \rightarrow \; Distance \; you \; traveled \; by \; walk \; in \; miles \\ d_c \; \rightarrow \; Distance \; traveled \; by \; your \; friend \; using \; bicycle \; in \; miles \\ t \; \rightarrow \; Time \; Taken \; in \; hours [/tex]
Step 2: List the given details
Distance between you and your friend is 12 miles. It means the total distance traveled by you by walk and your friend using bicycle when both travel towards each other to meet in 't' hours
Equation 1:
[tex] d_w+d_c=12 [/tex]
Your Walking rate and your friends Cycling rate is given below:
[tex] r_w=4mph\\r_c=11mph [/tex]
Step 3: Set up an equation using the relationship between distance, time and rate.
[tex] Distance=Rate \times Time [/tex]
[tex] d_w=r_w \times t=4t \\\\ d_c = r_c \times t = 11t [/tex]
Substituting the above in equation 1
[tex] 4t+11t=12 \\ Combining \; Like \; Terms \\\\ 15t=12 \\ Dividing \; 15 \; on \; both \; sides \\\\ 15t \div 15=12 \div 15 \\\\ t=0.8 hours [/tex]
Distance traveled by you by walking from home and distance travelled by your friend in cycle in 0.8 hours is given below:
[tex] d_w=4t=4(0.8)=3.2miles \\\\ d_c=11t=11(0.8)=8.8miles [/tex]
