SOLUTION: to recieve their beans from their manufacturer, tamara and michael must meet the dilivery truck whil it is completing its route. the distance from the coffee house to the manufactu

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Question 846795: to recieve their beans from their manufacturer, tamara and michael must meet the dilivery truck whil it is completing its route. the distance from the coffee house to the manufacturers's warehouse where the truck starts its journey is 90km.. they know they can drive 20km/h faster that the delivery truck. a. if they leave at the same time as the delivery truck and meet it half an hour later, how far away from the manufacturers warehouse will they meet. b.tamara and michael wish to open their coffee house every morning at 8:30am. if they have to pick upa weeks supply of beans every friday morning when will they have to leave to be back in time to open the coffee house?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Part (a):
The delivery truck drives in one direction on a pathway and the shop owners drive in the opposite direction. Sum of the distances traveled would be 90 km. MEET after 1%2F2 hour.

Vehicle________speed_______time___________distance
Truck___________r__________1/2____________r(1/2)
Tam&Michael____r+20________1/2____________(r+20)(1/2)
Total_____________________________________90

Find truck speed.
highlight_green%28r%2F2%2B%28r%2B20%29%2F2=90%29------based on the total distances each travel
r%2Br%2B20=180
2r%2B20=180
2r=160
highlight%28r=80%29 km per hour
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Meeting happens 40 km from the warehouse.
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That was for part (a). It ONLY USES one equation to solve the the unknown variable r. You would then simply use R*T=D (Rate, Time, Distance) to find the distances; in this case, the distance from the warehouse where the owners meet the truck, which is simple 80%2A%28km%2Fhour%29%2A%281%2F2%29%2Ahour=highlight%2840%2Akm%29.
You can also easily get the speed of Tamara & Michael, because if they move 20 km/hour faster than the truck, then their speed is 80%2B20=highlight%28100%29.

Part (b) is too open-ended. Is it supposed to be so? Does it have some further constraining information given? TOO, too, openended.
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NEW THOUGHT:
Maybe this part need not be so open-ended. ASSUMING the truck would leave its warehouse in time to be 40 km from warehouse at a time a little before 7:30AM, then Tamara and Michael could make that distance in the half-hour specified for part (a). their round-trip to pickup the coffee beans would allow them to be able to return by 8:30AM with their supply of beans.