Irving lives in Appletown, and plans to drive along Highway 42, a straight highway that leads to Bananatown, located 143 miles east and 45 miles north. Carol lives in Coconutville, located 98 miles east and 32 miles south of Appletown. Highway 86 runs directly north from Coconutville, and junctions with Highway 42 before heading further north to Durianville. Carol and Irving are planning to meet up at park-and-ride at the junction of the highways and carpool to Bananatown. Irving leaves Appletown at 8am, driving his usual 45 miles per hour. If Carol leaves Coconutville at 9am, how fast will she need to drive to arrive at the park-and-ride the same time as Irving?

Answer:

The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time is approximately 47.188 miles per hour

Step-by-step explanation:

The given information are;

The location of Bananatown from Appletown = 143 miles east and 45 miles north

The location of Coconutville from Appletown = 98 miles east and 32 miles south

Taking Appletown as the origin, we have;

The slope, gradient of highway 42 = 45/143

The equation of a line representing highway 42 is given as follows;

y - 0 = 45/143 × (x - 0)

y = 45/143·x

Therefore, at Coconutville, where x = 98, we have, y = 45/143 × 98 ≈ 30.84 miles north

Total distance north Carol has to drive to get to highway 42 = 32 + 30.84 = 62.84 miles

Total distance along highway 42 Carol will drive to get to Bananatown = √((143 - 98)² + (45 - 30.84)²) ≈ 47.175 miles

Total distance Carol drives to Bananatown = 47.175 miles + 62.84 miles ≈ 110.015 miles

The total distance Irvin needs to drive to arrive at Bananatown = √(143² + 45²) ≈ 149.91

The total distance Irvin needs to drive to arrive at Bananatown ≈ 149.91  miles

The time it takes Irvin to arrive at Bananatown = (149.91 miles)/(45 mph) ≈  3.33 hours

The time he arrives at Bananatown = 8 a.m. + 3.33 hours ≈ 11.33 a.m.

The time available for Carol to meet Irvin at Bananatown at exactly the same time = 11.33 a.m. - 9 a.m. = 2.33 hours

Therefore, the speed at which Carol needs to drive = (110.015 miles)/2.33 hour ≈ 47.188 miles per hour

The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time ≈ 47.188 miles per hour.

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