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jeka94
3 years ago
13

You and your friend live 12 miles apart. you leave home at the same time and travel ttoward eacth other.you walk at the rate of

4 miles per hour and your friend bycicles at a rate of 11 mile per hour. how long after you leave home will you meet? how far from home will each of you be
Mathematics
1 answer:
mr Goodwill [35]3 years ago
8 0

Step 1: Assign variable for the unknown that  you need to find.

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

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:

d_w+d_c=12

Your Walking rate and your friends Cycling rate is given below:

r_w=4mph\\r_c=11mph

Step 3: Set up an equation using the relationship between distance, time and rate.

Distance=Rate \times Time

d_w=r_w \times t=4t \\\\ d_c = r_c \times t = 11t

Substituting the above in equation 1

4t+11t=12 \\ Combining \; Like \; Terms \\\\ 15t=12 \\ Dividing \; 15 \; on \; both \; sides \\\\ 15t \div 15=12 \div 15 \\\\ t=0.8 hours

Distance traveled by you by walking from home and distance travelled by your friend in cycle in 0.8 hours is given below:

d_w=4t=4(0.8)=3.2miles \\\\ d_c=11t=11(0.8)=8.8miles

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