Question

Destiny is eating lunch at her favorite cafe when her friend Jada calls and says she wants to meet her. Jada is calling from a city 45 miles away and wants to meet Destiny somewhere between the two locations. Jada says she will start driving right away, but Destiny needs 10 min to finish her lunch before she can begin driving. Jada plans to drive at 55 mph, whereas Destiny usually averages about 70 mph. Ignore acceleration and assume the highway is a straight line.

Required:
a. How many minutes from will Jada be driving before she meets Destiny?
b. How many miles d will Destiny have traveled when they meet?

Answer 1

Answer:

Explanation:

Let time taken by Jada in driving be t hour .

distance travelled by jada = 55 t

a )

Time of drive by destiny = t - 10 min

= t - .167 hour

distance of travel by destiny = 70 ( t - .167 )

Total distance = 45 miles

55 t + 70 ( t - .167 ) = 45

55t + 70 t - 11.69 = 45

125 t = 56.69

t = .453 hour = 27.21 minutes

b )

distance travelled by Destiny = 70 ( t - .167 )

70 ( .453 - .167 )

= 20.02 miles .

Answer 2

a. The number of time in minutes that Jada would drive before she meets Destiny is 27.204 minutes.

b. The distance traveled by Destiny when they meet is 20.069 miles.

• Let Jada's driving time be t.

Given the following data:

• Jada's distance = 45 miles.

• Jada's speed = 55 mph.

• Destiny's speed = 70 mph.

Conversion:

Destiny's lunch time = 10 mins to hr = 0.1667 hour.

How to determine time and speed.

Mathematically, speed is given by this formula;

$Speed = \frac{distance}{time}$

a. To calculate the number of time in minutes that Jada would drive before she meets Destiny:

Note: Destiny's drive time is equal to $t - 0.1667$ hour.

For Jada's distance:

$Distance = speed \times time\\\\Distance = 55t\;miles$

For Destiny's distance:

$Distance = speed \times time\\\\Distance = 70(t-0.1667)\;miles$

Mathematically, the total distance traveled by Jada is given by:

$55t+70(t-0.1667)=45\\\\55t+70t-11.669=45\\\\125t=45+11.669\\\\125t=33.331\\\\t=\frac{56.669}{125}$

t = 0.4534 hours.

In minutes:

Time, t = $0.4534 \times 60$ = 27.204 minutes.

b. To calculate the distance traveled by Destiny when they meet:

$Distance =70(t-0.1667)\\\\Distance =70(0.4534-0.1667)\\\\Distance =70 \times 0.2867$

Distance = 20.069 miles.

Learn more about distance here: https://brainly.com/question/10545161