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 By: griniegenie (offline)  Friday, August 15 2014 @ 01:32 AM CDT (Read 1372 times)
griniegenie

Hi all,
need help in these 2 qns~

Car X and Car Y started travelling at 0945 from opposite ends of a straight road.
Car X travelled at an average speed of 80 km/h.
Car Y travelled 20 km/h faster and took 3/4 hour less than Car X to travel the entire distance.
Find the time when both cars met.

A pharmacist paid \$2363 for some bottles of vitamins and fish oil. He bought four times as many bottles of fish oil as vitamins.
Each bottle of fish oil cost \$19 less than each bottle of vitamins. He spent \$901 more on the fish oil than on the vitamins.
How much does each bottle of vitamins cost?

Newbie

Registered: 12/31/06
Posts: 4

 By: echeewh (offline)  Friday, August 15 2014 @ 06:55 PM CDT
echeewh

Hey <griniegenie>

Appreciate that you can provide <Answerkey> in future, if any. Thanks.

Following are my worked solutions:

Q1

s(X) : s(Y)
80 : 100
4 : 5

Given that distance is constant, the time taken ratio is the reverse / inverse of the speed ratio. Hence,

t(X) : t(Y)
5 : 4

1u --> (3/4)hr

To travel the entire distance,
X took 5u --> 5 × (3/4) = (15/4)hr

Y took 4u --> 4 × (3/4) = 3hr

Hence, distance = 80 × (15/4) = 300 km

t(when both cars met) = Distance Apart ÷ Sum of Speeds
= 300 ÷ 180 = (5/3) hr = 1 hr 40 min

Time (when both X, Y met):
09 45 + 1 40 = 11 25

=========

Q2.

<Cost>

V |------------|
F |------------<- 901 ->|

Given that both vitamins (V) and fish Oil (F) cost \$2363, we have ...

2u --> 2363 - 901 = 1462
1u --> 1462 ÷ 2 = 731

hence, F = 731 + 901 = 1632 ; V = 731

Given number of bottles bought,
F : V
4 : 1

4u (F) --> 1632
1u (F) --> 408

1u (V) --> 731

Given each bottle of fish oil (F) cost \$19 less than each bottle of vitamins (V),
V - F = 19

Cost Difference between 1u of V and 1u of F:
731 - 408 = 323

Number of bottles of V:
323 ÷ 19 = 17

Cost of 1 bottle of V:
731 ÷ 17 = \$43

==========

Trust these help.

Do let me know again if these are different from your <Answerkey> or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: griniegenie (offline)  Monday, August 18 2014 @ 11:15 PM CDT
griniegenie

Thank you soo much for answering!
Qns were given without answers.. =(

Newbie

Registered: 12/31/06
Posts: 4

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