Question

Ryan and Janelle are each driving from a different location to meet.When they each stopped for lunch at 12 noon,they called each other on their cell phones.Ryan had traveled 245 miles in 3 1/2 hours.Janelle had driven 260 miles in 4 hours.If Ryan and Janelle were originally 910 miles apart when they had started driving that morning,at what time will they meet?

Answer 1

They will meet at 3:00 p.m.

Since Ryan traveled 245 miles in 3.5 hours, he traveled at a speed of 245/3.5=70 mph.  Janelle traveled 260 miles in 4 hours; she traveled at a speed of 260/4=65 mph.

Together, they had traveled 245+260=505 miles by noon.  This leaves 910-505=405 miles to travel.

If Ryan stays at a constant rate of 70 mph, his distance is given by 70t.  If Janelle stays at a constant rate of 65 mph, her distance is given by 65t.  Their distances together equal 405:
70t+65t = 405

Combining like terms, 

135t = 405

Divide both sides by 135:
135t/135 = 405/135
t = 3

3 hours after noon will be 3:00 p.m.

Answer 2

Speed is the ratio of the distance travelled by the object and the time taken by the object. Ryan and Janelle will meet at 3 pm.

What is speed?

speed can be defined as the rate of change of position of an object with respect to time. It is the ratio of the distance travelled by the object and the time taken by the object.

As the distance travelled by Ryan is 245 miles in 3 1/2 hours. Therefore, the speed of Ryan can be written as,

$Speed= \dfrac{Distance}{Time}\\\\Speed= \dfrac{245}{3.5}\\\\Speed= 70\rm\ miles/ hour$

As the distance travelled by Janelle is 260 miles in 4 hours. Therefore, the speed of Janelle can be written as,

$Speed= \dfrac{Distance}{Time}\\\\Speed= \dfrac{260}{4}\\\\Speed= 65\rm\ miles/ hour$

Now, The distance that is left between both of them can be written as,

The distance that is left between both of them =

Total Distance - Distance travelled by Ryan - Distance travelled by Janelle

$=910-245-260\\=405\rm\ miles$

Further, as the distance between them is 405 miles while they both are travelling towards each other, therefore, their speed will be added together to complete the distance between them,

Thus, the time is taken to cover the distance between them,

$Speed= \dfrac{Distance}{Time}\\\\Time= \dfrac{Distance}{Speed}\\\\\\Time= \dfrac{405}{65+70}\\\\\\Time= 3\rm\ hour$

Hence, they will meet after 3 hours, therefore, Ryan and Janelle will meet at 3 pm.

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