Question

(20%) problem 7: your uncle is trying to convince you join his research team at cern by offering you a summer job that pays a wage of w = 11 € (euro) per hour. the lab is d = 7.4 km from your uncle's house, where you would be staying. you know that you can bike 1 mile in t = 6 minutes. alternatively, you can borrow your uncle's car as long as you pay for gasoline. the car's gas tank has a capacity of c = 13 us gallons, and the price of gasoline is p = 1.41 €/liter.

Answer 1

Solution:

A)

Expected hourly income in $US  = rate * hourly income in Euro

= 1.2903 * 13 = $16.7739

B)

Time taken from uncle's house to lab = Distance /Speed

Distance is  8.5 km  

Speed is 1mile in 5 minutes  

 Hence converting mile in Kilometer = 1.609344 km in 5 minutes  

 distance traveled in an hour = 1.609344 *12 =19.312128

 Time = 8.5/19.312128  = 0.44013792783 hours = 26.408 minutes

 

C)

Capacity =13 US gallons  

1US gallon = 3.78541 litre

Hence 13 gallons = 13 * 3.78541

=49.21033 litres

 

D)

Gasoline = 1.41 Euro /litre

= 1.2903 * 1.41 = 1.819323 $ /litre

Hence 1 litre = 1.819323 dollar

1 gallon = 3.78541 litre  = 6.88688347743 dollar

Hence price = 6.88688347743 dollar /gallon

E)

we can travel 20 miles in 1 gallon  

= 1.609344*20 km  

capacity of tank =13 gallons  

total distance that can be traveled in 13 gallons = 1.609344*20*13 km = 418.42944 km  

days that can be traveled  = 418.42944/8.5 = 49.2269929412 days = 49 days

Answer 2

Since the distance has been provided, the number of days used will be 28 days.

How to find the number of days

From the complete question, given that the car drives 20 miles per gallon, and the tank capacity is 13 gallons, therefore the distance covered with a full tank will be:

= 20 × 13 = 260 miles.

Note that 1 mile = 1.609km

In this case, the distance between the house and the laboratory is 7.4km and he will commute twice per day. This will be:

= 7.4 × 2 = 14.8 km

Therefore, the total number of days that he can commute will be:

= (260 × 1.609) / 14.8

= 28 days.

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