Question

Jordan and Roman travel the same route to work. Jordan leaves for work one morning and drives at a rate, r, of 56 mph. Roman leaves the house soon after, when Jordan has already traveled 2 mi. Roman drives at a rate of 60 mph. How long after Jordan leaves home will Roman catch up to her? How many miles into their commute will this occur?

Answer 1

recall your d = rt, distance = rate * time

by the time Roman catches up with Jordan, the distance travelled by both is exactly the same, since both vehicles are meeting, say they had travelled "d" miles.

By the time Roman takes off, Jordan is already rolling for 2miles...hmmm how many minutes is that? well, she's doing 56 miles for 60 minutes, so


`\bf \begin{array}{ccllll} miles&minutes\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 56&60\\ 2&m \end{array}\implies \cfrac{56}{2}=\cfrac{60}{m}\implies m=\cfrac{120}{56}\implies m=\cfrac{15}{7}`

so, she's been driving for 15/7 minutes already, thus

bear in mind that, if they meet at "t" minutes, Roman has been driving 15/7 minutes less than Jordan.


`\bf \begin{cases} \boxed{d}=56t\\ d=60\left( t-(15)/(7) \right)\\ ----------\\ \boxed{56t}=60\left( t-(15)/(7) \right) \end{cases} \\\\\\ 56t=60t-\cfrac{900}{7}\implies \cfrac{900}{7}=60t-56t \\\\\\ \cfrac{900}{7}=4t\implies \cfrac{900}{28}=t\implies 32.14\approx t`

so, they meet 32 minutes and about 8 seconds later.

how many miles is that? well, Jordan is doing 56 miles for 60 minutes, how much is is for 32.14 minutes?


`\bf \begin{array}{ccllll} miles&minutes\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 56&60\\ x&32.14 \end{array}\implies \cfrac{56}{x}=\cfrac{60}{32.14}\implies \cfrac{32.14\cdot 56}{60}=x\\\\\\ 29.997 \approx x`

so, roughly about 30 miles down the road.

Answer 2

Answer: d = 56t

d = 60t – 2

Step-by-step explanation:

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